diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences.py b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences.py
new file mode 100644
index 0000000..a0bb3cc
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences.py
@@ -0,0 +1,409 @@
+"""Up-tooth apex colour sequences of Kempe-balanced 3-colourings.
+
+Companion experiment to ``kempe_valid_colorings.py``.  For a fixed annular
+size ``n`` and a fixed number ``m`` of up teeth we:
+
+  1. generate every full medial tire graph M(T) with |A(T)| = n and exactly
+     ``m`` up teeth (one representative per dihedral symmetry class);
+  2. enumerate the Kempe-balanced (``valid``) proper 3-colourings of each M(T)
+     and read off the colour sequence of the up-tooth apex vertices u0 < u1 <
+     ... in increasing annular-edge order (i.e. cyclic order around A(T));
+  3. reduce each up-tooth sequence modulo the six colour permutations -- but
+     NOT modulo the dihedral symmetry of the cycle -- to a canonical sequence;
+  4. group the M(T) by the *set* of canonical up-tooth sequences they realise,
+     and report how many M(T) share each set.
+
+For every canonical up-tooth sequence we emit a markdown note listing every
+M(T) that realises it together with every Kempe-balanced colouring (modulo
+colour permutation) on that M(T) producing the sequence, and a figure drawing
+those colourings.  A summary note records the step-4 grouping.
+
+Run:  python3 kempe_up_tooth_sequences.py --n 9 --m 4
+"""
+
+from __future__ import annotations
+
+import argparse
+import math
+import os
+from collections import defaultdict
+
+from full_medial_tire_generator import FullMedialTireGraph, generate
+from kempe_valid_colorings import (
+    adjacency,
+    classify_colorings,
+    kempe_components,
+)
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+
+Coloring = dict[str, int]
+PALETTE = {0: "#e6550d", 1: "#3182bd", 2: "#31a354"}
+PALETTE_NAME = {0: "orange", 1: "blue", 2: "green"}
+
+
+def canonical_sequence(seq: tuple[int, ...]) -> tuple[int, ...]:
+    """Relabel a colour sequence by first appearance (mod colour permutation)."""
+    remap: dict[int, int] = {}
+    out = []
+    for c in seq:
+        if c not in remap:
+            remap[c] = len(remap)
+        out.append(remap[c])
+    return tuple(out)
+
+
+def seq_str(seq: tuple[int, ...]) -> str:
+    return "".join(str(c) for c in seq)
+
+
+def _parity_partitions(m: int) -> set[tuple[int, ...]]:
+    """Colour multisets (n0,n1,n2) of m up-tooth apexes admissible under the
+    outer-face Kempe-parity rule: all three counts share m's parity.  Returned
+    as tuples of the nonzero parts (descending), matching the table format."""
+    out: set[tuple[int, ...]] = set()
+    for a in range(m + 1):
+        for b in range(a + 1):
+            c = m - a - b
+            if c < 0 or c > b:
+                continue
+            if a % 2 == b % 2 == c % 2 == m % 2:
+                out.add(tuple(v for v in (a, b, c) if v > 0))
+    return out
+
+
+def up_tooth_sequence(graph: FullMedialTireGraph, coloring: Coloring) -> tuple[int, ...]:
+    """Colours of the up-tooth apexes in increasing annular-edge order."""
+    return tuple(coloring[f"u{i}"] for i in graph.up_edges)
+
+
+def graph_id(idx: int) -> str:
+    return f"G{idx:02d}"
+
+
+def describe_graph(graph: FullMedialTireGraph) -> str:
+    bites = ",".join(f"({i},{j})" for i, j in sorted(graph.bites)) or "-"
+    return f"word={graph.tooth_word} bites={bites}"
+
+
+# ---------------------------------------------------------------------------
+# Data collection.
+# ---------------------------------------------------------------------------
+
+class Experiment:
+    def __init__(self, n: int, m: int):
+        self.n = n
+        self.m = m
+        self.graphs: list[FullMedialTireGraph] = [
+            g for g in generate(n, min_up_teeth=3, dedup=True) if len(g.up_edges) == m
+        ]
+        # per graph: list of (coloring, canonical up-tooth sequence)
+        self.colorings: list[list[tuple[Coloring, tuple[int, ...]]]] = []
+        # per graph: set of canonical up-tooth sequences it realises
+        self.graph_seq_sets: list[frozenset[tuple[int, ...]]] = []
+        # canonical sequence -> list of (graph_idx, coloring)
+        self.by_sequence: dict[tuple[int, ...], list[tuple[int, Coloring]]] = defaultdict(list)
+
+        for gidx, g in enumerate(self.graphs):
+            entries: list[tuple[Coloring, tuple[int, ...]]] = []
+            seqs: set[tuple[int, ...]] = set()
+            for coloring, verdict in classify_colorings(g, dedup_colors=True):
+                if not verdict.valid:
+                    continue
+                cseq = canonical_sequence(up_tooth_sequence(g, coloring))
+                entries.append((coloring, cseq))
+                seqs.add(cseq)
+                self.by_sequence[cseq].append((gidx, coloring))
+            self.colorings.append(entries)
+            self.graph_seq_sets.append(frozenset(seqs))
+
+    def groups(self):
+        """Map each set-of-sequences to the list of graph indices realising it."""
+        groups: dict[frozenset[tuple[int, ...]], list[int]] = defaultdict(list)
+        for gidx, sset in enumerate(self.graph_seq_sets):
+            groups[sset].append(gidx)
+        # sort by descending membership, then by set size
+        return sorted(groups.items(), key=lambda kv: (-len(kv[1]), len(kv[0])))
+
+    def sequences(self) -> list[tuple[int, ...]]:
+        return sorted(self.by_sequence)
+
+
+# ---------------------------------------------------------------------------
+# Drawing (adapted from kempe_valid_colorings._draw_colored).
+# ---------------------------------------------------------------------------
+
+def _positions(graph: FullMedialTireGraph) -> dict[str, tuple[float, float]]:
+    n = graph.n
+
+    def ann_xy(k):
+        ang = math.pi / 2 - 2 * math.pi * k / n
+        return math.cos(ang), math.sin(ang)
+
+    def mid_ang(i):
+        return math.pi / 2 - 2 * math.pi * (i + 0.5) / n
+
+    pos = {f"a{k}": ann_xy(k) for k in range(n)}
+    matched = graph.bite_edges
+    for i, tooth in enumerate(graph.tooth_word):
+        if tooth == "U":
+            pos[f"u{i}"] = (1.42 * math.cos(mid_ang(i)), 1.42 * math.sin(mid_ang(i)))
+        elif i not in matched:
+            pos[f"d{i}"] = (0.58 * math.cos(mid_ang(i)), 0.58 * math.sin(mid_ang(i)))
+    for i, j in sorted(graph.bites):
+        corners = [ann_xy(i), ann_xy((i + 1) % n), ann_xy(j), ann_xy((j + 1) % n)]
+        cx = sum(p[0] for p in corners) / 4.0
+        cy = sum(p[1] for p in corners) / 4.0
+        pos[f"p{i}_{j}"] = (cx * 0.82, cy * 0.82)
+    return pos
+
+
+def _draw(ax, graph, coloring, title):
+    pos = _positions(graph)
+    for u, v in graph.edges():
+        ax.plot([pos[u][0], pos[v][0]], [pos[u][1], pos[v][1]],
+                color="#bbbbbb", lw=0.5, zorder=1)
+    for k in range(graph.n):
+        a, b = f"a{k}", f"a{(k + 1) % graph.n}"
+        ax.plot([pos[a][0], pos[b][0]], [pos[a][1], pos[b][1]],
+                color="#666666", lw=1.0, zorder=2)
+    for v, (x, y) in pos.items():
+        is_bite = v.startswith("p")
+        ax.scatter([x], [y], s=34 if is_bite else 24, color=PALETTE[coloring[v]],
+                   edgecolors="black", linewidths=0.5 if is_bite else 0.3, zorder=3)
+    # ring the up-tooth apexes whose colours form the recorded sequence
+    ux = [pos[f"u{i}"][0] for i in graph.up_edges]
+    uy = [pos[f"u{i}"][1] for i in graph.up_edges]
+    ax.scatter(ux, uy, s=120, facecolors="none", edgecolors="#222222",
+               linewidths=1.4, zorder=4)
+    ax.set_xlim(-1.65, 1.65)
+    ax.set_ylim(-1.85, 1.65)
+    ax.set_aspect("equal")
+    ax.axis("off")
+    ax.set_title(title, fontsize=6, pad=1.5)
+
+
+def draw_sequence(exp: Experiment, seq, out_png, out_pdf):
+    import matplotlib
+    matplotlib.use("Agg")
+    import matplotlib.pyplot as plt
+
+    entries = exp.by_sequence[seq]
+    cols = 10
+    rows = math.ceil(len(entries) / cols)
+    fig, axes = plt.subplots(rows, cols, figsize=(cols * 1.5, rows * 1.7), squeeze=False)
+    for idx in range(rows * cols):
+        ax = axes[idx // cols][idx % cols]
+        if idx < len(entries):
+            gidx, coloring = entries[idx]
+            g = exp.graphs[gidx]
+            useq = seq_str(up_tooth_sequence(g, coloring))
+            _draw(ax, g, coloring, f"{graph_id(gidx)}  u={useq}")
+        else:
+            ax.axis("off")
+    fig.suptitle(
+        f"Kempe-balanced colourings with up-tooth apex sequence "
+        f"{seq_str(seq)} (mod colour permutation)\n"
+        f"n={exp.n}, m={exp.m} up teeth — {len(entries)} colourings on "
+        f"{len({g for g, _ in entries})} M(T); black rings mark up-tooth apexes",
+        fontsize=11, y=0.998,
+    )
+    fig.tight_layout(rect=(0, 0, 1, 0.96))
+    fig.savefig(out_png, dpi=170)
+    fig.savefig(out_pdf)
+    plt.close(fig)
+    print(f"wrote {out_png}")
+
+
+# ---------------------------------------------------------------------------
+# Markdown notes.
+# ---------------------------------------------------------------------------
+
+def compact_coloring(graph: FullMedialTireGraph, coloring: Coloring) -> str:
+    """A readable one-line dump of the full colouring, grouped by vertex kind."""
+    parts = []
+    parts.append("A=" + "".join(str(coloring[f"a{k}"]) for k in range(graph.n)))
+    up = " ".join(f"u{i}:{coloring[f'u{i}']}" for i in graph.up_edges)
+    parts.append("U[" + up + "]")
+    downs = []
+    for i in graph.singleton_down_edges:
+        downs.append(f"d{i}:{coloring[f'd{i}']}")
+    for i, j in sorted(graph.bites):
+        downs.append(f"p{i}_{j}:{coloring[f'p{i}_{j}']}")
+    if downs:
+        parts.append("D[" + " ".join(downs) + "]")
+    return "  ".join(parts)
+
+
+def write_sequence_note(exp: Experiment, seq, path, fig_name):
+    s = seq_str(seq)
+    # group entries by graph
+    by_graph: dict[int, list[Coloring]] = defaultdict(list)
+    for gidx, coloring in exp.by_sequence[seq]:
+        by_graph[gidx].append(coloring)
+
+    colour_multiset = {}
+    for c in seq:
+        colour_multiset[c] = colour_multiset.get(c, 0) + 1
+    counts = ", ".join(f"{n}×colour{c}" for c, n in sorted(colour_multiset.items()))
+
+    lines = []
+    lines.append(f"# Up-tooth apex sequence `{s}`")
+    lines.append("")
+    lines.append(
+        f"Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic "
+        f"order around A(T), reduced modulo the six colour permutations) for "
+        f"Kempe-balanced 3-colourings of M(T) with **n = {exp.n}**, "
+        f"**m = {exp.m} up teeth**."
+    )
+    lines.append("")
+    lines.append(f"- Colour multiset: {counts}.")
+    lines.append(f"- Realised by **{len(by_graph)}** of {len(exp.graphs)} M(T) "
+                 f"(dihedral classes).")
+    lines.append(f"- **{len(exp.by_sequence[seq])}** Kempe-balanced colourings "
+                 f"(mod colour permutation) produce it.")
+    lines.append(f"- Figure: `{fig_name}` (black rings mark the up-tooth apexes).")
+    lines.append("")
+    lines.append("Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` "
+                 "up-tooth apexes; `D[...]` singleton down apexes `d` and bite "
+                 "apexes `p`. Colours are 0/1/2 = "
+                 + ", ".join(f"{c}:{PALETTE_NAME[c]}" for c in (0, 1, 2)) + ".")
+    lines.append("")
+    for gidx in sorted(by_graph):
+        g = exp.graphs[gidx]
+        cols = by_graph[gidx]
+        lines.append(f"## {graph_id(gidx)} — {describe_graph(g)}")
+        lines.append("")
+        lines.append(f"{len(cols)} colouring(s) with up-tooth sequence `{s}`:")
+        lines.append("")
+        for coloring in cols:
+            raw = seq_str(up_tooth_sequence(g, coloring))
+            lines.append(f"- up apexes (raw labels) `{raw}` → canonical `{s}`  ·  "
+                         f"`{compact_coloring(g, coloring)}`")
+        lines.append("")
+    with open(path, "w") as fh:
+        fh.write("\n".join(lines) + "\n")
+    print(f"wrote {path}")
+
+
+def write_summary(exp: Experiment, path, notes_dir_name):
+    lines = []
+    lines.append(f"# Up-tooth apex sequences of Kempe-balanced colourings "
+                 f"(n={exp.n}, m={exp.m})")
+    lines.append("")
+    lines.append(
+        f"Every full medial tire graph M(T) with |A(T)| = {exp.n} and exactly "
+        f"{exp.m} up teeth, one representative per dihedral class: "
+        f"**{len(exp.graphs)} M(T)**. For each we enumerate the Kempe-balanced "
+        f"(valid) proper 3-colourings (modulo colour permutation), read the "
+        f"up-tooth apex colour sequence u0<u1<... in cyclic order, and reduce it "
+        f"modulo colour permutation (NOT dihedral symmetry)."
+    )
+    lines.append("")
+    total = sum(len(c) for c in exp.colorings)
+    lines.append(f"- Total Kempe-balanced colourings (mod colour permutation): "
+                 f"**{total}**.")
+    lines.append(f"- Distinct canonical up-tooth sequences overall: "
+                 f"**{len(exp.by_sequence)}**.")
+    lines.append("")
+    lines.append("## Distinct canonical up-tooth sequences")
+    lines.append("")
+    lines.append("| sequence | colour multiset | #M(T) realising | #colourings |")
+    lines.append("|---|---|---|---|")
+    for seq in exp.sequences():
+        cm = {}
+        for c in seq:
+            cm[c] = cm.get(c, 0) + 1
+        cms = "+".join(str(v) for v in sorted(cm.values(), reverse=True))
+        ngraphs = len({g for g, _ in exp.by_sequence[seq]})
+        lines.append(f"| `{seq_str(seq)}` | {cms} | {ngraphs} | "
+                     f"{len(exp.by_sequence[seq])} |")
+    lines.append("")
+    # The outer-face Kempe-parity rule says every colour pair meets the up-tooth
+    # apexes an even number of times; equivalently the three colour-counts share
+    # one parity.  With m apexes that parity is forced by m mod 2.
+    parity = "even" if exp.m % 2 == 0 else "odd"
+    allowed = sorted(
+        {"+".join(str(v) for v in sorted(p, reverse=True))
+         for p in _parity_partitions(exp.m)}
+    )
+    lines.append("Note: every realised sequence has its three colour-counts of "
+                 "**equal parity** — exactly the outer-face Kempe-parity "
+                 "constraint (each colour pair meets the up-tooth apexes an even "
+                 f"number of times). With m = {exp.m} up teeth (m is "
+                 f"{'even' if exp.m % 2 == 0 else 'odd'}) every count must be "
+                 f"**{parity}**, so the only admissible colour multisets are "
+                 + ", ".join(allowed) + ".")
+    lines.append("")
+    lines.append("## Step 4 — grouping M(T) by their set of unique up-tooth "
+                 "sequences")
+    lines.append("")
+    groups = exp.groups()
+    lines.append(f"The {len(exp.graphs)} M(T) fall into **{len(groups)}** groups "
+                 f"by the set of canonical up-tooth sequences they realise:")
+    lines.append("")
+    lines.append("| #M(T) | set of up-tooth sequences | M(T) ids |")
+    lines.append("|---|---|---|")
+    for sset, gidxs in groups:
+        seqs = ", ".join(f"`{seq_str(s)}`" for s in sorted(sset))
+        ids = ", ".join(graph_id(i) for i in gidxs)
+        lines.append(f"| {len(gidxs)} | {{ {seqs} }} | {ids} |")
+    lines.append("")
+    lines.append("## M(T) atlas (ids)")
+    lines.append("")
+    lines.append("| id | word / bites | #Kempe-balanced | up-tooth sequence set |")
+    lines.append("|---|---|---|---|")
+    for gidx, g in enumerate(exp.graphs):
+        sset = exp.graph_seq_sets[gidx]
+        seqs = ", ".join(f"`{seq_str(s)}`" for s in sorted(sset))
+        lines.append(f"| {graph_id(gidx)} | {describe_graph(g)} | "
+                     f"{len(exp.colorings[gidx])} | {{ {seqs} }} |")
+    lines.append("")
+    lines.append("## Per-sequence notes")
+    lines.append("")
+    for seq in exp.sequences():
+        lines.append(f"- [`{seq_str(seq)}`](seq_{seq_str(seq)}.md) — "
+                     f"figure `seq_{seq_str(seq)}.png`")
+    lines.append("")
+    with open(path, "w") as fh:
+        fh.write("\n".join(lines) + "\n")
+    print(f"wrote {path}")
+
+
+# ---------------------------------------------------------------------------
+# Driver.
+# ---------------------------------------------------------------------------
+
+def run(args):
+    exp = Experiment(args.n, args.m)
+    print(f"n={args.n}, m={args.m}: {len(exp.graphs)} M(T) (dihedral classes)")
+    print(f"distinct canonical up-tooth sequences: {len(exp.by_sequence)}")
+    for seq in exp.sequences():
+        ng = len({g for g, _ in exp.by_sequence[seq]})
+        print(f"  {seq_str(seq)}: {ng} M(T), {len(exp.by_sequence[seq])} colourings")
+    print(f"groups by sequence-set: {len(exp.groups())}")
+
+    notes_dir = os.path.join(HERE, f"kempe_up_tooth_sequences_n{args.n}_m{args.m}")
+    os.makedirs(notes_dir, exist_ok=True)
+
+    write_summary(exp, os.path.join(notes_dir, "summary.md"), notes_dir)
+    for seq in exp.sequences():
+        s = seq_str(seq)
+        fig_name = f"seq_{s}.png"
+        write_sequence_note(exp, seq, os.path.join(notes_dir, f"seq_{s}.md"), fig_name)
+        if not args.no_figures:
+            draw_sequence(exp, seq,
+                          os.path.join(notes_dir, fig_name),
+                          os.path.join(notes_dir, f"seq_{s}.pdf"))
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--n", type=int, default=9)
+    parser.add_argument("--m", type=int, default=4, help="number of up teeth")
+    parser.add_argument("--no-figures", action="store_true")
+    run(parser.parse_args())
+
+
+if __name__ == "__main__":
+    main()
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m3/seq_012.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m3/seq_012.md
new file mode 100644
index 0000000..7389ff1
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m3/seq_012.md
@@ -0,0 +1,325 @@
+# Up-tooth apex sequence `012`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 3 up teeth**.
+
+- Colour multiset: 1×colour0, 1×colour1, 1×colour2.
+- Realised by **23** of 23 M(T) (dihedral classes).
+- **199** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_012.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUDDDDDD bites=-
+
+22 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010101  U[u0:2 u1:0 u2:1]  D[d3:2 d4:2 d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010102  U[u0:2 u1:0 u2:1]  D[d3:2 d4:2 d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010121  U[u0:2 u1:0 u2:1]  D[d3:2 d4:2 d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010201  U[u0:2 u1:0 u2:1]  D[d3:2 d4:2 d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010202  U[u0:2 u1:0 u2:1]  D[d3:2 d4:2 d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010212  U[u0:2 u1:0 u2:1]  D[d3:2 d4:2 d5:1 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012012  U[u0:2 u1:0 u2:1]  D[d3:2 d4:0 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012021  U[u0:2 u1:0 u2:1]  D[d3:2 d4:0 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012101  U[u0:2 u1:0 u2:1]  D[d3:2 d4:0 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012102  U[u0:2 u1:0 u2:1]  D[d3:2 d4:0 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012121  U[u0:2 u1:0 u2:1]  D[d3:2 d4:0 d5:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020101  U[u0:2 u1:0 u2:1]  D[d3:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020102  U[u0:2 u1:0 u2:1]  D[d3:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020121  U[u0:2 u1:0 u2:1]  D[d3:1 d4:1 d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020201  U[u0:2 u1:0 u2:1]  D[d3:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u2:1]  D[d3:1 d4:1 d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u2:1]  D[d3:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021012  U[u0:2 u1:0 u2:1]  D[d3:1 d4:0 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021021  U[u0:2 u1:0 u2:1]  D[d3:1 d4:0 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021201  U[u0:2 u1:0 u2:1]  D[d3:1 d4:0 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021202  U[u0:2 u1:0 u2:1]  D[d3:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021212  U[u0:2 u1:0 u2:1]  D[d3:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
+
+## G01 — word=UUUDDDDDD bites=(3,8)
+
+12 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010101  U[u0:2 u1:0 u2:1]  D[d4:2 d5:2 d6:2 d7:2 p3_8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010121  U[u0:2 u1:0 u2:1]  D[d4:2 d5:2 d6:0 d7:0 p3_8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010201  U[u0:2 u1:0 u2:1]  D[d4:2 d5:1 d6:1 d7:2 p3_8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012021  U[u0:2 u1:0 u2:1]  D[d4:0 d5:1 d6:1 d7:0 p3_8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012101  U[u0:2 u1:0 u2:1]  D[d4:0 d5:0 d6:2 d7:2 p3_8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012121  U[u0:2 u1:0 u2:1]  D[d4:0 d5:0 d6:0 d7:0 p3_8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020102  U[u0:2 u1:0 u2:1]  D[d4:1 d5:2 d6:2 d7:1 p3_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u2:1]  D[d4:1 d5:1 d6:1 d7:1 p3_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u2:1]  D[d4:1 d5:1 d6:0 d7:0 p3_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021012  U[u0:2 u1:0 u2:1]  D[d4:0 d5:2 d6:2 d7:0 p3_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021202  U[u0:2 u1:0 u2:1]  D[d4:0 d5:0 d6:1 d7:1 p3_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021212  U[u0:2 u1:0 u2:1]  D[d4:0 d5:0 d6:0 d7:0 p3_8:1]`
+
+## G02 — word=UUDUDDDDD bites=-
+
+11 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020101  U[u0:2 u1:0 u3:1]  D[d2:1 d4:1 d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020102  U[u0:2 u1:0 u3:1]  D[d2:1 d4:1 d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020121  U[u0:2 u1:0 u3:1]  D[d2:1 d4:1 d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020201  U[u0:2 u1:0 u3:1]  D[d2:1 d4:1 d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u3:1]  D[d2:1 d4:1 d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u3:1]  D[d2:1 d4:1 d5:1 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021012  U[u0:2 u1:0 u3:1]  D[d2:1 d4:0 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021021  U[u0:2 u1:0 u3:1]  D[d2:1 d4:0 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021201  U[u0:2 u1:0 u3:1]  D[d2:1 d4:0 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021202  U[u0:2 u1:0 u3:1]  D[d2:1 d4:0 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021212  U[u0:2 u1:0 u3:1]  D[d2:1 d4:0 d5:0 d6:0 d7:0 d8:1]`
+
+## G03 — word=UUDUDDDDD bites=(2,4)
+
+6 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020101  U[u0:2 u1:0 u3:1]  D[d5:2 d6:2 d7:2 d8:2 p2_4:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020102  U[u0:2 u1:0 u3:1]  D[d5:2 d6:2 d7:1 d8:1 p2_4:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020121  U[u0:2 u1:0 u3:1]  D[d5:2 d6:0 d7:0 d8:2 p2_4:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020201  U[u0:2 u1:0 u3:1]  D[d5:1 d6:1 d7:2 d8:2 p2_4:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u3:1]  D[d5:1 d6:1 d7:1 d8:1 p2_4:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u3:1]  D[d5:1 d6:0 d7:0 d8:1 p2_4:1]`
+
+## G04 — word=UUDUDDDDD bites=(2,8)
+
+6 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020102  U[u0:2 u1:0 u3:1]  D[d4:1 d5:2 d6:2 d7:1 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u3:1]  D[d4:1 d5:1 d6:1 d7:1 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u3:1]  D[d4:1 d5:1 d6:0 d7:0 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021012  U[u0:2 u1:0 u3:1]  D[d4:0 d5:2 d6:2 d7:0 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021202  U[u0:2 u1:0 u3:1]  D[d4:0 d5:0 d6:1 d7:1 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012021212  U[u0:2 u1:0 u3:1]  D[d4:0 d5:0 d6:0 d7:0 p2_8:1]`
+
+## G05 — word=UUDDUDDDD bites=-
+
+17 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020101  U[u0:2 u1:0 u4:1]  D[d2:1 d3:1 d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020102  U[u0:2 u1:0 u4:1]  D[d2:1 d3:1 d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020121  U[u0:2 u1:0 u4:1]  D[d2:1 d3:1 d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020201  U[u0:2 u1:0 u4:1]  D[d2:1 d3:1 d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u4:1]  D[d2:1 d3:1 d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u4:1]  D[d2:1 d3:1 d5:1 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102012  U[u0:2 u1:0 u4:1]  D[d2:0 d3:2 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102021  U[u0:2 u1:0 u4:1]  D[d2:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102101  U[u0:2 u1:0 u4:1]  D[d2:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102102  U[u0:2 u1:0 u4:1]  D[d2:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102121  U[u0:2 u1:0 u4:1]  D[d2:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120101  U[u0:2 u1:0 u4:1]  D[d2:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120102  U[u0:2 u1:0 u4:1]  D[d2:0 d3:0 d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120121  U[u0:2 u1:0 u4:1]  D[d2:0 d3:0 d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u1:0 u4:1]  D[d2:0 d3:0 d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u1:0 u4:1]  D[d2:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120212  U[u0:2 u1:0 u4:1]  D[d2:0 d3:0 d5:1 d6:0 d7:0 d8:1]`
+
+## G06 — word=UUDDUDDDD bites=(3,5)
+
+3 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020201  U[u0:2 u1:0 u4:1]  D[d2:1 d6:1 d7:2 d8:2 p3_5:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u4:1]  D[d2:1 d6:1 d7:1 d8:1 p3_5:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u4:1]  D[d2:1 d6:0 d7:0 d8:1 p3_5:1]`
+
+## G07 — word=UUDDUDDDD bites=(2,8)
+
+3 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020102  U[u0:2 u1:0 u4:1]  D[d3:1 d5:2 d6:2 d7:1 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u4:1]  D[d3:1 d5:1 d6:1 d7:1 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u4:1]  D[d3:1 d5:1 d6:0 d7:0 p2_8:1]`
+
+## G08 — word=UUDDDUDDD bites=-
+
+13 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010201  U[u0:2 u1:0 u5:1]  D[d2:1 d3:2 d4:2 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010202  U[u0:2 u1:0 u5:1]  D[d2:1 d3:2 d4:2 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010212  U[u0:2 u1:0 u5:1]  D[d2:1 d3:2 d4:2 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012012  U[u0:2 u1:0 u5:1]  D[d2:1 d3:2 d4:0 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012021  U[u0:2 u1:0 u5:1]  D[d2:1 d3:2 d4:0 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020201  U[u0:2 u1:0 u5:1]  D[d2:1 d3:1 d4:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u5:1]  D[d2:1 d3:1 d4:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u5:1]  D[d2:1 d3:1 d4:1 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102012  U[u0:2 u1:0 u5:1]  D[d2:0 d3:2 d4:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102021  U[u0:2 u1:0 u5:1]  D[d2:0 d3:2 d4:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u1:0 u5:1]  D[d2:0 d3:0 d4:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u1:0 u5:1]  D[d2:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120212  U[u0:2 u1:0 u5:1]  D[d2:0 d3:0 d4:1 d6:0 d7:0 d8:1]`
+
+## G09 — word=UUDDDUDDD bites=(4,6)
+
+5 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020201  U[u0:2 u1:0 u5:1]  D[d2:1 d3:1 d7:2 d8:2 p4_6:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u5:1]  D[d2:1 d3:1 d7:1 d8:1 p4_6:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102021  U[u0:2 u1:0 u5:1]  D[d2:0 d3:2 d7:0 d8:2 p4_6:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u1:0 u5:1]  D[d2:0 d3:0 d7:2 d8:2 p4_6:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u1:0 u5:1]  D[d2:0 d3:0 d7:1 d8:1 p4_6:1]`
+
+## G10 — word=UUDDDUDDD bites=(2,8)
+
+5 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010202  U[u0:2 u1:0 u5:1]  D[d3:2 d4:2 d6:1 d7:1 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012010212  U[u0:2 u1:0 u5:1]  D[d3:2 d4:2 d6:0 d7:0 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012012012  U[u0:2 u1:0 u5:1]  D[d3:2 d4:0 d6:2 d7:0 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u5:1]  D[d3:1 d4:1 d6:1 d7:1 p2_8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020212  U[u0:2 u1:0 u5:1]  D[d3:1 d4:1 d6:0 d7:0 p2_8:1]`
+
+## G11 — word=UUDDDUDDD bites=(2,8),(3,7),(4,6)
+
+1 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012020202  U[u0:2 u1:0 u5:1]  D[p2_8:1 p3_7:1 p4_6:1]`
+
+## G12 — word=UDUDUDDDD bites=-
+
+26 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212012  U[u0:2 u2:1 u4:0]  D[d1:2 d3:0 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212021  U[u0:2 u2:1 u4:0]  D[d1:2 d3:0 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212101  U[u0:2 u2:1 u4:0]  D[d1:2 d3:0 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212102  U[u0:2 u2:1 u4:0]  D[d1:2 d3:0 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212121  U[u0:2 u2:1 u4:0]  D[d1:2 d3:0 d5:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012012  U[u0:2 u2:1 u4:0]  D[d1:0 d3:2 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012021  U[u0:2 u2:1 u4:0]  D[d1:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012101  U[u0:2 u2:1 u4:0]  D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012102  U[u0:2 u2:1 u4:0]  D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012121  U[u0:2 u2:1 u4:0]  D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021012  U[u0:2 u2:1 u4:0]  D[d1:0 d3:1 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021021  U[u0:2 u2:1 u4:0]  D[d1:0 d3:1 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021201  U[u0:2 u2:1 u4:0]  D[d1:0 d3:1 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021202  U[u0:2 u2:1 u4:0]  D[d1:0 d3:1 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021212  U[u0:2 u2:1 u4:0]  D[d1:0 d3:1 d5:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102012  U[u0:2 u2:0 u4:1]  D[d1:0 d3:2 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102021  U[u0:2 u2:0 u4:1]  D[d1:0 d3:2 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102101  U[u0:2 u2:0 u4:1]  D[d1:0 d3:2 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102102  U[u0:2 u2:0 u4:1]  D[d1:0 d3:2 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102121  U[u0:2 u2:0 u4:1]  D[d1:0 d3:2 d5:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120101  U[u0:2 u2:0 u4:1]  D[d1:0 d3:0 d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120102  U[u0:2 u2:0 u4:1]  D[d1:0 d3:0 d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120121  U[u0:2 u2:0 u4:1]  D[d1:0 d3:0 d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u2:0 u4:1]  D[d1:0 d3:0 d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u2:0 u4:1]  D[d1:0 d3:0 d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120212  U[u0:2 u2:0 u4:1]  D[d1:0 d3:0 d5:1 d6:0 d7:0 d8:1]`
+
+## G13 — word=UDUDUDDDD bites=(3,5)
+
+3 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212101  U[u0:2 u2:1 u4:0]  D[d1:2 d6:2 d7:2 d8:2 p3_5:0]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212102  U[u0:2 u2:1 u4:0]  D[d1:2 d6:2 d7:1 d8:1 p3_5:0]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212121  U[u0:2 u2:1 u4:0]  D[d1:2 d6:0 d7:0 d8:2 p3_5:0]`
+
+## G14 — word=UDUDUDDDD bites=(1,3)
+
+6 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120101  U[u0:2 u2:0 u4:1]  D[d5:2 d6:2 d7:2 d8:2 p1_3:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120102  U[u0:2 u2:0 u4:1]  D[d5:2 d6:2 d7:1 d8:1 p1_3:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120121  U[u0:2 u2:0 u4:1]  D[d5:2 d6:0 d7:0 d8:2 p1_3:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u2:0 u4:1]  D[d5:1 d6:1 d7:2 d8:2 p1_3:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u2:0 u4:1]  D[d5:1 d6:1 d7:1 d8:1 p1_3:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120212  U[u0:2 u2:0 u4:1]  D[d5:1 d6:0 d7:0 d8:1 p1_3:0]`
+
+## G15 — word=UDUDDUDDD bites=-
+
+20 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010201201  U[u0:2 u2:1 u5:0]  D[d1:2 d3:1 d4:2 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010201202  U[u0:2 u2:1 u5:0]  D[d1:2 d3:1 d4:2 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010201212  U[u0:2 u2:1 u5:0]  D[d1:2 d3:1 d4:2 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010202101  U[u0:2 u2:1 u5:0]  D[d1:2 d3:1 d4:1 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010202102  U[u0:2 u2:1 u5:0]  D[d1:2 d3:1 d4:1 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010202121  U[u0:2 u2:1 u5:0]  D[d1:2 d3:1 d4:1 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212101  U[u0:2 u2:1 u5:0]  D[d1:2 d3:0 d4:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212102  U[u0:2 u2:1 u5:0]  D[d1:2 d3:0 d4:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212121  U[u0:2 u2:1 u5:0]  D[d1:2 d3:0 d4:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012101  U[u0:2 u2:1 u5:0]  D[d1:0 d3:2 d4:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012102  U[u0:2 u2:1 u5:0]  D[d1:0 d3:2 d4:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012121  U[u0:2 u2:1 u5:0]  D[d1:0 d3:2 d4:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021201  U[u0:2 u2:1 u5:0]  D[d1:0 d3:1 d4:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021202  U[u0:2 u2:1 u5:0]  D[d1:0 d3:1 d4:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021212  U[u0:2 u2:1 u5:0]  D[d1:0 d3:1 d4:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102012  U[u0:2 u2:0 u5:1]  D[d1:0 d3:2 d4:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102021  U[u0:2 u2:0 u5:1]  D[d1:0 d3:2 d4:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u2:0 u5:1]  D[d1:0 d3:0 d4:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u2:0 u5:1]  D[d1:0 d3:0 d4:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120212  U[u0:2 u2:0 u5:1]  D[d1:0 d3:0 d4:1 d6:0 d7:0 d8:1]`
+
+## G16 — word=UDUDDUDDD bites=(4,6)
+
+6 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212121  U[u0:2 u2:1 u5:0]  D[d1:2 d3:0 d7:0 d8:2 p4_6:0]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012012121  U[u0:2 u2:1 u5:0]  D[d1:0 d3:2 d7:0 d8:2 p4_6:0]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021212  U[u0:2 u2:1 u5:0]  D[d1:0 d3:1 d7:0 d8:1 p4_6:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012102021  U[u0:2 u2:0 u5:1]  D[d1:0 d3:2 d7:0 d8:2 p4_6:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u2:0 u5:1]  D[d1:0 d3:0 d7:2 d8:2 p4_6:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u2:0 u5:1]  D[d1:0 d3:0 d7:1 d8:1 p4_6:1]`
+
+## G17 — word=UDUDDUDDD bites=(1,3)
+
+3 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u2:0 u5:1]  D[d4:1 d6:1 d7:2 d8:2 p1_3:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u2:0 u5:1]  D[d4:1 d6:1 d7:1 d8:1 p1_3:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120212  U[u0:2 u2:0 u5:1]  D[d4:1 d6:0 d7:0 d8:1 p1_3:0]`
+
+## G18 — word=UDUDDUDDD bites=(1,8)
+
+5 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010201201  U[u0:2 u2:1 u5:0]  D[d3:1 d4:2 d6:1 d7:2 p1_8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010202101  U[u0:2 u2:1 u5:0]  D[d3:1 d4:1 d6:2 d7:2 p1_8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010202121  U[u0:2 u2:1 u5:0]  D[d3:1 d4:1 d6:0 d7:0 p1_8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212101  U[u0:2 u2:1 u5:0]  D[d3:0 d4:0 d6:2 d7:2 p1_8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212121  U[u0:2 u2:1 u5:0]  D[d3:0 d4:0 d6:0 d7:0 p1_8:2]`
+
+## G19 — word=UDUDDUDDD bites=(1,8),(3,7),(4,6)
+
+1 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010212121  U[u0:2 u2:1 u5:0]  D[p1_8:2 p3_7:0 p4_6:0]`
+
+## G20 — word=UDDUDDUDD bites=-
+
+18 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010120201  U[u0:2 u3:0 u6:1]  D[d1:2 d2:2 d4:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010120202  U[u0:2 u3:0 u6:1]  D[d1:2 d2:2 d4:1 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010121021  U[u0:2 u3:0 u6:1]  D[d1:2 d2:2 d4:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010121201  U[u0:2 u3:0 u6:1]  D[d1:2 d2:2 d4:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010121202  U[u0:2 u3:0 u6:1]  D[d1:2 d2:2 d4:0 d5:0 d7:1 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010201212  U[u0:2 u3:1 u6:0]  D[d1:2 d2:1 d4:2 d5:0 d7:0 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010202121  U[u0:2 u3:1 u6:0]  D[d1:2 d2:1 d4:1 d5:0 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010210201  U[u0:2 u3:0 u6:1]  D[d1:2 d2:1 d4:2 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010210202  U[u0:2 u3:0 u6:1]  D[d1:2 d2:1 d4:2 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010212021  U[u0:2 u3:0 u6:1]  D[d1:2 d2:1 d4:0 d5:1 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012020121  U[u0:2 u3:1 u6:0]  D[d1:0 d2:1 d4:1 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012020212  U[u0:2 u3:1 u6:0]  D[d1:0 d2:1 d4:1 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021212  U[u0:2 u3:1 u6:0]  D[d1:0 d2:1 d4:0 d5:0 d7:0 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120201  U[u0:2 u3:0 u6:1]  D[d1:0 d2:0 d4:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u3:0 u6:1]  D[d1:0 d2:0 d4:1 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012121021  U[u0:2 u3:0 u6:1]  D[d1:0 d2:0 d4:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012121201  U[u0:2 u3:0 u6:1]  D[d1:0 d2:0 d4:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012121202  U[u0:2 u3:0 u6:1]  D[d1:0 d2:0 d4:0 d5:0 d7:1 d8:1]`
+
+## G21 — word=UDDUDDUDD bites=(5,7)
+
+6 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010120202  U[u0:2 u3:0 u6:1]  D[d1:2 d2:2 d4:1 d8:1 p5_7:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010201212  U[u0:2 u3:1 u6:0]  D[d1:2 d2:1 d4:2 d8:1 p5_7:0]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010202121  U[u0:2 u3:1 u6:0]  D[d1:2 d2:1 d4:1 d8:2 p5_7:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=010210202  U[u0:2 u3:0 u6:1]  D[d1:2 d2:1 d4:2 d8:1 p5_7:1]`
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=012021212  U[u0:2 u3:1 u6:0]  D[d1:0 d2:1 d4:0 d8:1 p5_7:0]`
+- up apexes (raw labels) `201` → canonical `012`  ·  `A=012120202  U[u0:2 u3:0 u6:1]  D[d1:0 d2:0 d4:1 d8:1 p5_7:1]`
+
+## G22 — word=UDDUDDUDD bites=(1,8),(2,4),(5,7)
+
+1 colouring(s) with up-tooth sequence `012`:
+
+- up apexes (raw labels) `210` → canonical `012`  ·  `A=010202121  U[u0:2 u3:1 u6:0]  D[p1_8:2 p2_4:1 p5_7:0]`
+
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m3/summary.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m3/summary.md
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+# Up-tooth apex sequences of Kempe-balanced colourings (n=9, m=3)
+
+Every full medial tire graph M(T) with |A(T)| = 9 and exactly 3 up teeth, one representative per dihedral class: **23 M(T)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the up-tooth apex colour sequence u0<u1<... in cyclic order, and reduce it modulo colour permutation (NOT dihedral symmetry).
+
+- Total Kempe-balanced colourings (mod colour permutation): **199**.
+- Distinct canonical up-tooth sequences overall: **1**.
+
+## Distinct canonical up-tooth sequences
+
+| sequence | colour multiset | #M(T) realising | #colourings |
+|---|---|---|---|
+| `012` | 1+1+1 | 23 | 199 |
+
+Note: every realised sequence has its three colour-counts of **equal parity** — exactly the outer-face Kempe-parity constraint (each colour pair meets the up-tooth apexes an even number of times). With m = 3 up teeth (m is odd) every count must be **odd**, so the only admissible colour multisets are 1+1+1.
+
+## Step 4 — grouping M(T) by their set of unique up-tooth sequences
+
+The 23 M(T) fall into **1** groups by the set of canonical up-tooth sequences they realise:
+
+| #M(T) | set of up-tooth sequences | M(T) ids |
+|---|---|---|
+| 23 | { `012` } | G00, G01, G02, G03, G04, G05, G06, G07, G08, G09, G10, G11, G12, G13, G14, G15, G16, G17, G18, G19, G20, G21, G22 |
+
+## M(T) atlas (ids)
+
+| id | word / bites | #Kempe-balanced | up-tooth sequence set |
+|---|---|---|---|
+| G00 | word=UUUDDDDDD bites=- | 22 | { `012` } |
+| G01 | word=UUUDDDDDD bites=(3,8) | 12 | { `012` } |
+| G02 | word=UUDUDDDDD bites=- | 11 | { `012` } |
+| G03 | word=UUDUDDDDD bites=(2,4) | 6 | { `012` } |
+| G04 | word=UUDUDDDDD bites=(2,8) | 6 | { `012` } |
+| G05 | word=UUDDUDDDD bites=- | 17 | { `012` } |
+| G06 | word=UUDDUDDDD bites=(3,5) | 3 | { `012` } |
+| G07 | word=UUDDUDDDD bites=(2,8) | 3 | { `012` } |
+| G08 | word=UUDDDUDDD bites=- | 13 | { `012` } |
+| G09 | word=UUDDDUDDD bites=(4,6) | 5 | { `012` } |
+| G10 | word=UUDDDUDDD bites=(2,8) | 5 | { `012` } |
+| G11 | word=UUDDDUDDD bites=(2,8),(3,7),(4,6) | 1 | { `012` } |
+| G12 | word=UDUDUDDDD bites=- | 26 | { `012` } |
+| G13 | word=UDUDUDDDD bites=(3,5) | 3 | { `012` } |
+| G14 | word=UDUDUDDDD bites=(1,3) | 6 | { `012` } |
+| G15 | word=UDUDDUDDD bites=- | 20 | { `012` } |
+| G16 | word=UDUDDUDDD bites=(4,6) | 6 | { `012` } |
+| G17 | word=UDUDDUDDD bites=(1,3) | 3 | { `012` } |
+| G18 | word=UDUDDUDDD bites=(1,8) | 5 | { `012` } |
+| G19 | word=UDUDDUDDD bites=(1,8),(3,7),(4,6) | 1 | { `012` } |
+| G20 | word=UDDUDDUDD bites=- | 18 | { `012` } |
+| G21 | word=UDDUDDUDD bites=(5,7) | 6 | { `012` } |
+| G22 | word=UDDUDDUDD bites=(1,8),(2,4),(5,7) | 1 | { `012` } |
+
+## Per-sequence notes
+
+- [`012`](seq_012.md) — figure `seq_012.png`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0000.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0000.md
new file mode 100644
index 0000000..2df9349
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0000.md
@@ -0,0 +1,221 @@
+# Up-tooth apex sequence `0000`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 up teeth**.
+
+- Colour multiset: 4×colour0.
+- Realised by **27** of 29 M(T) (dihedral classes).
+- **75** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_0000.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUDDDDD bites=-
+
+10 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u3:2]  D[d4:2 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u2:2 u3:2]  D[d4:2 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101201  U[u0:2 u1:2 u2:2 u3:2]  D[d4:2 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101202  U[u0:2 u1:2 u2:2 u3:2]  D[d4:2 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101212  U[u0:2 u1:2 u2:2 u3:2]  D[d4:2 d5:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102012  U[u0:2 u1:2 u2:2 u3:2]  D[d4:1 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102021  U[u0:2 u1:2 u2:2 u3:2]  D[d4:1 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102101  U[u0:2 u1:2 u2:2 u3:2]  D[d4:1 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102102  U[u0:2 u1:2 u2:2 u3:2]  D[d4:1 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102121  U[u0:2 u1:2 u2:2 u3:2]  D[d4:1 d5:0 d6:0 d7:0 d8:2]`
+
+## G01 — word=UUUUDDDDD bites=(4,8)
+
+4 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u2:2 u3:2]  D[d5:2 d6:1 d7:0 p4_8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101201  U[u0:2 u1:2 u2:2 u3:2]  D[d5:0 d6:1 d7:2 p4_8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102012  U[u0:2 u1:2 u2:2 u3:2]  D[d5:1 d6:2 d7:0 p4_8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102102  U[u0:2 u1:2 u2:2 u3:2]  D[d5:0 d6:2 d7:1 p4_8:1]`
+
+## G02 — word=UUUDUDDDD bites=-
+
+5 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u4:2]  D[d3:2 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u2:2 u4:2]  D[d3:2 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101201  U[u0:2 u1:2 u2:2 u4:2]  D[d3:2 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101202  U[u0:2 u1:2 u2:2 u4:2]  D[d3:2 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101212  U[u0:2 u1:2 u2:2 u4:2]  D[d3:2 d5:0 d6:0 d7:0 d8:1]`
+
+## G03 — word=UUUDUDDDD bites=(3,5)
+
+2 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u4:2]  D[d6:2 d7:0 d8:1 p3_5:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u2:2 u4:2]  D[d6:1 d7:0 d8:2 p3_5:2]`
+
+## G04 — word=UUUDUDDDD bites=(3,8)
+
+2 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u2:2 u4:2]  D[d5:2 d6:1 d7:0 p3_8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101201  U[u0:2 u1:2 u2:2 u4:2]  D[d5:0 d6:1 d7:2 p3_8:2]`
+
+## G05 — word=UUUDDUDDD bites=-
+
+7 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u5:2]  D[d3:2 d4:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u2:2 u5:2]  D[d3:2 d4:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010120101  U[u0:2 u1:2 u2:2 u5:2]  D[d3:0 d4:1 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010120102  U[u0:2 u1:2 u2:2 u5:2]  D[d3:0 d4:1 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010120121  U[u0:2 u1:2 u2:2 u5:2]  D[d3:0 d4:1 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010121012  U[u0:2 u1:2 u2:2 u5:2]  D[d3:0 d4:0 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010121021  U[u0:2 u1:2 u2:2 u5:2]  D[d3:0 d4:0 d6:1 d7:0 d8:2]`
+
+## G06 — word=UUUDDUDDD bites=(4,6)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u5:2]  D[d3:2 d7:0 d8:1 p4_6:2]`
+
+## G07 — word=UUUDDUDDD bites=(3,8)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u2:2 u5:2]  D[d4:2 d6:1 d7:0 p3_8:2]`
+
+## G08 — word=UUDUUDDDD bites=-
+
+5 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u3:2 u4:2]  D[d2:2 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u3:2 u4:2]  D[d2:2 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101201  U[u0:2 u1:2 u3:2 u4:2]  D[d2:2 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101202  U[u0:2 u1:2 u3:2 u4:2]  D[d2:2 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101212  U[u0:2 u1:2 u3:2 u4:2]  D[d2:2 d5:0 d6:0 d7:0 d8:1]`
+
+## G09 — word=UUDUUDDDD bites=(2,5)
+
+2 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u3:2 u4:2]  D[d6:2 d7:0 d8:1 p2_5:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u3:2 u4:2]  D[d6:1 d7:0 d8:2 p2_5:2]`
+
+## G10 — word=UUDUDUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u3:2 u5:2]  D[d2:2 d4:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u3:2 u5:2]  D[d2:2 d4:2 d6:1 d7:0 d8:2]`
+
+## G11 — word=UUDUDUDDD bites=(4,6)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u3:2 u5:2]  D[d2:2 d7:0 d8:1 p4_6:2]`
+
+## G12 — word=UUDUDUDDD bites=(2,4)
+
+2 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u3:2 u5:2]  D[d6:2 d7:0 d8:1 p2_4:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u3:2 u5:2]  D[d6:1 d7:0 d8:2 p2_4:2]`
+
+## G13 — word=UUDUDUDDD bites=(2,8)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u3:2 u5:2]  D[d4:2 d6:1 d7:0 p2_8:2]`
+
+## G14 — word=UUDUDDUDD bites=-
+
+4 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u3:2 u6:2]  D[d2:2 d4:2 d5:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102012  U[u0:2 u1:2 u3:2 u6:2]  D[d2:2 d4:1 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102101  U[u0:2 u1:2 u3:2 u6:2]  D[d2:2 d4:1 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102102  U[u0:2 u1:2 u3:2 u6:2]  D[d2:2 d4:1 d5:0 d7:1 d8:1]`
+
+## G16 — word=UUDUDDUDD bites=(2,4)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u3:2 u6:2]  D[d5:2 d7:0 d8:1 p2_4:2]`
+
+## G17 — word=UUDUDDUDD bites=(2,8)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102101  U[u0:2 u1:2 u3:2 u6:2]  D[d4:1 d5:0 d7:2 p2_8:2]`
+
+## G18 — word=UUDUDDDUD bites=-
+
+2 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101201  U[u0:2 u1:2 u3:2 u7:2]  D[d2:2 d4:2 d5:0 d6:1 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102101  U[u0:2 u1:2 u3:2 u7:2]  D[d2:2 d4:1 d5:0 d6:2 d8:2]`
+
+## G19 — word=UUDUDDDUD bites=(6,8)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102101  U[u0:2 u1:2 u3:2 u7:2]  D[d2:2 d4:1 d5:0 p6_8:2]`
+
+## G20 — word=UUDUDDDUD bites=(2,8)
+
+2 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101201  U[u0:2 u1:2 u3:2 u7:2]  D[d4:2 d5:0 d6:1 p2_8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010102101  U[u0:2 u1:2 u3:2 u7:2]  D[d4:1 d5:0 d6:2 p2_8:2]`
+
+## G21 — word=UUDDUUDDD bites=-
+
+7 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u4:2 u5:2]  D[d2:2 d3:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101021  U[u0:2 u1:2 u4:2 u5:2]  D[d2:2 d3:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010201012  U[u0:2 u1:2 u4:2 u5:2]  D[d2:1 d3:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010201021  U[u0:2 u1:2 u4:2 u5:2]  D[d2:1 d3:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010210101  U[u0:2 u1:2 u4:2 u5:2]  D[d2:1 d3:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010210102  U[u0:2 u1:2 u4:2 u5:2]  D[d2:1 d3:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010210121  U[u0:2 u1:2 u4:2 u5:2]  D[d2:1 d3:0 d6:0 d7:0 d8:2]`
+
+## G22 — word=UUDDUUDDD bites=(3,6)
+
+3 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u4:2 u5:2]  D[d2:2 d7:0 d8:1 p3_6:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010201021  U[u0:2 u1:2 u4:2 u5:2]  D[d2:1 d7:0 d8:2 p3_6:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010210121  U[u0:2 u1:2 u4:2 u5:2]  D[d2:1 d7:0 d8:2 p3_6:0]`
+
+## G23 — word=UUDDUDUDD bites=-
+
+4 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u1:2 u4:2 u6:2]  D[d2:2 d3:2 d5:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010201012  U[u0:2 u1:2 u4:2 u6:2]  D[d2:1 d3:1 d5:2 d7:0 d8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010210101  U[u0:2 u1:2 u4:2 u6:2]  D[d2:1 d3:0 d5:2 d7:2 d8:2]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010210102  U[u0:2 u1:2 u4:2 u6:2]  D[d2:1 d3:0 d5:2 d7:1 d8:1]`
+
+## G24 — word=UUDDUDUDD bites=(5,7)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010210101  U[u0:2 u1:2 u4:2 u6:2]  D[d2:1 d3:0 d8:2 p5_7:2]`
+
+## G25 — word=UUDDUDUDD bites=(2,8)
+
+2 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010201012  U[u0:2 u1:2 u4:2 u6:2]  D[d3:1 d5:2 d7:0 p2_8:1]`
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010210102  U[u0:2 u1:2 u4:2 u6:2]  D[d3:0 d5:2 d7:1 p2_8:1]`
+
+## G26 — word=UDUDUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u2:2 u4:2 u6:2]  D[d1:2 d3:2 d5:2 d7:0 d8:1]`
+
+## G28 — word=UDUDUDUDD bites=(3,5)
+
+1 colouring(s) with up-tooth sequence `0000`:
+
+- up apexes (raw labels) `2222` → canonical `0000`  ·  `A=010101012  U[u0:2 u2:2 u4:2 u6:2]  D[d1:2 d7:0 d8:1 p3_5:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0000.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0000.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0000.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0000.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0011.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0011.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0011.md
@@ -0,0 +1,296 @@
+# Up-tooth apex sequence `0011`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1.
+- Realised by **29** of 29 M(T) (dihedral classes).
+- **140** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_0011.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUDDDDD bites=-
+
+10 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201012  U[u0:2 u1:2 u2:1 u3:1]  D[d4:2 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201021  U[u0:2 u1:2 u2:1 u3:1]  D[d4:2 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201201  U[u0:2 u1:2 u2:1 u3:1]  D[d4:2 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201202  U[u0:2 u1:2 u2:1 u3:1]  D[d4:2 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201212  U[u0:2 u1:2 u2:1 u3:1]  D[d4:2 d5:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u2:1 u3:1]  D[d4:1 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u3:1]  D[d4:1 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202101  U[u0:2 u1:2 u2:1 u3:1]  D[d4:1 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202102  U[u0:2 u1:2 u2:1 u3:1]  D[d4:1 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202121  U[u0:2 u1:2 u2:1 u3:1]  D[d4:1 d5:0 d6:0 d7:0 d8:2]`
+
+## G01 — word=UUUUDDDDD bites=(4,8)
+
+4 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201021  U[u0:2 u1:2 u2:1 u3:1]  D[d5:2 d6:1 d7:0 p4_8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201201  U[u0:2 u1:2 u2:1 u3:1]  D[d5:0 d6:1 d7:2 p4_8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u2:1 u3:1]  D[d5:1 d6:2 d7:0 p4_8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202102  U[u0:2 u1:2 u2:1 u3:1]  D[d5:0 d6:2 d7:1 p4_8:1]`
+
+## G02 — word=UUUDUDDDD bites=-
+
+5 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u2:1 u4:1]  D[d3:1 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u4:1]  D[d3:1 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202101  U[u0:2 u1:2 u2:1 u4:1]  D[d3:1 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202102  U[u0:2 u1:2 u2:1 u4:1]  D[d3:1 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202121  U[u0:2 u1:2 u2:1 u4:1]  D[d3:1 d5:0 d6:0 d7:0 d8:2]`
+
+## G03 — word=UUUDUDDDD bites=(3,5)
+
+2 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u2:1 u4:1]  D[d6:2 d7:0 d8:1 p3_5:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u4:1]  D[d6:1 d7:0 d8:2 p3_5:1]`
+
+## G04 — word=UUUDUDDDD bites=(3,8)
+
+2 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u2:1 u4:1]  D[d5:1 d6:2 d7:0 p3_8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202102  U[u0:2 u1:2 u2:1 u4:1]  D[d5:0 d6:2 d7:1 p3_8:1]`
+
+## G05 — word=UUUDDUDDD bites=-
+
+7 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u2:1 u5:1]  D[d3:1 d4:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u5:1]  D[d3:1 d4:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010210201  U[u0:2 u1:2 u2:1 u5:1]  D[d3:0 d4:2 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010210202  U[u0:2 u1:2 u2:1 u5:1]  D[d3:0 d4:2 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010210212  U[u0:2 u1:2 u2:1 u5:1]  D[d3:0 d4:2 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010212012  U[u0:2 u1:2 u2:1 u5:1]  D[d3:0 d4:0 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010212021  U[u0:2 u1:2 u2:1 u5:1]  D[d3:0 d4:0 d6:1 d7:0 d8:2]`
+
+## G06 — word=UUUDDUDDD bites=(4,6)
+
+1 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u5:1]  D[d3:1 d7:0 d8:2 p4_6:1]`
+
+## G07 — word=UUUDDUDDD bites=(3,8)
+
+1 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u2:1 u5:1]  D[d4:1 d6:2 d7:0 p3_8:1]`
+
+## G08 — word=UUDUUDDDD bites=-
+
+15 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121012  U[u0:2 u1:2 u3:0 u4:0]  D[d2:2 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121021  U[u0:2 u1:2 u3:0 u4:0]  D[d2:2 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121201  U[u0:2 u1:2 u3:0 u4:0]  D[d2:2 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121202  U[u0:2 u1:2 u3:0 u4:0]  D[d2:2 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u3:0 u4:0]  D[d2:2 d5:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u3:1 u4:1]  D[d2:1 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u3:1 u4:1]  D[d2:1 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202101  U[u0:2 u1:2 u3:1 u4:1]  D[d2:1 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202102  U[u0:2 u1:2 u3:1 u4:1]  D[d2:1 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202121  U[u0:2 u1:2 u3:1 u4:1]  D[d2:1 d5:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212012  U[u0:2 u1:2 u3:0 u4:0]  D[d2:1 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212021  U[u0:2 u1:2 u3:0 u4:0]  D[d2:1 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212101  U[u0:2 u1:2 u3:0 u4:0]  D[d2:1 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212102  U[u0:2 u1:2 u3:0 u4:0]  D[d2:1 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u3:0 u4:0]  D[d2:1 d5:0 d6:0 d7:0 d8:2]`
+
+## G09 — word=UUDUUDDDD bites=(2,5)
+
+6 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121012  U[u0:2 u1:2 u3:0 u4:0]  D[d6:2 d7:0 d8:1 p2_5:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121021  U[u0:2 u1:2 u3:0 u4:0]  D[d6:1 d7:0 d8:2 p2_5:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u3:1 u4:1]  D[d6:2 d7:0 d8:1 p2_5:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u3:1 u4:1]  D[d6:1 d7:0 d8:2 p2_5:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212012  U[u0:2 u1:2 u3:0 u4:0]  D[d6:2 d7:0 d8:1 p2_5:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212021  U[u0:2 u1:2 u3:0 u4:0]  D[d6:1 d7:0 d8:2 p2_5:1]`
+
+## G10 — word=UUDUDUDDD bites=-
+
+8 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121201  U[u0:2 u1:2 u3:0 u5:0]  D[d2:2 d4:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121202  U[u0:2 u1:2 u3:0 u5:0]  D[d2:2 d4:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u3:0 u5:0]  D[d2:2 d4:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u3:1 u5:1]  D[d2:1 d4:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u3:1 u5:1]  D[d2:1 d4:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212101  U[u0:2 u1:2 u3:0 u5:0]  D[d2:1 d4:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212102  U[u0:2 u1:2 u3:0 u5:0]  D[d2:1 d4:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u3:0 u5:0]  D[d2:1 d4:0 d6:0 d7:0 d8:2]`
+
+## G11 — word=UUDUDUDDD bites=(4,6)
+
+3 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u3:0 u5:0]  D[d2:2 d7:0 d8:1 p4_6:0]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u3:1 u5:1]  D[d2:1 d7:0 d8:2 p4_6:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u3:0 u5:0]  D[d2:1 d7:0 d8:2 p4_6:0]`
+
+## G12 — word=UUDUDUDDD bites=(2,4)
+
+2 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u3:1 u5:1]  D[d6:2 d7:0 d8:1 p2_4:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u3:1 u5:1]  D[d6:1 d7:0 d8:2 p2_4:1]`
+
+## G13 — word=UUDUDUDDD bites=(2,8)
+
+3 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121201  U[u0:2 u1:2 u3:0 u5:0]  D[d4:0 d6:1 d7:2 p2_8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u3:1 u5:1]  D[d4:1 d6:2 d7:0 p2_8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212102  U[u0:2 u1:2 u3:0 u5:0]  D[d4:0 d6:2 d7:1 p2_8:1]`
+
+## G14 — word=UUDUDDUDD bites=-
+
+10 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010120121  U[u0:2 u1:2 u3:0 u6:0]  D[d2:2 d4:1 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010120212  U[u0:2 u1:2 u3:0 u6:0]  D[d2:2 d4:1 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u3:0 u6:0]  D[d2:2 d4:0 d5:0 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201021  U[u0:2 u1:2 u3:1 u6:1]  D[d2:1 d4:2 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201201  U[u0:2 u1:2 u3:1 u6:1]  D[d2:1 d4:2 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201202  U[u0:2 u1:2 u3:1 u6:1]  D[d2:1 d4:2 d5:0 d7:1 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u3:1 u6:1]  D[d2:1 d4:1 d5:1 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010210121  U[u0:2 u1:2 u3:0 u6:0]  D[d2:1 d4:2 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010210212  U[u0:2 u1:2 u3:0 u6:0]  D[d2:1 d4:2 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u3:0 u6:0]  D[d2:1 d4:0 d5:0 d7:0 d8:2]`
+
+## G15 — word=UUDUDDUDD bites=(5,7)
+
+2 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u3:0 u6:0]  D[d2:2 d4:0 d8:1 p5_7:0]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u3:0 u6:0]  D[d2:1 d4:0 d8:2 p5_7:0]`
+
+## G16 — word=UUDUDDUDD bites=(2,4)
+
+1 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u3:1 u6:1]  D[d5:1 d7:0 d8:2 p2_4:1]`
+
+## G17 — word=UUDUDDUDD bites=(2,8)
+
+3 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010120121  U[u0:2 u1:2 u3:0 u6:0]  D[d4:1 d5:2 d7:0 p2_8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201202  U[u0:2 u1:2 u3:1 u6:1]  D[d4:2 d5:0 d7:1 p2_8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010210212  U[u0:2 u1:2 u3:0 u6:0]  D[d4:2 d5:1 d7:0 p2_8:1]`
+
+## G18 — word=UUDUDDDUD bites=-
+
+12 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010120121  U[u0:2 u1:2 u3:0 u7:0]  D[d2:2 d4:1 d5:2 d6:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010120212  U[u0:2 u1:2 u3:0 u7:0]  D[d2:2 d4:1 d5:1 d6:0 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121012  U[u0:2 u1:2 u3:0 u7:0]  D[d2:2 d4:0 d5:2 d6:2 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121021  U[u0:2 u1:2 u3:0 u7:0]  D[d2:2 d4:0 d5:2 d6:1 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u3:0 u7:0]  D[d2:2 d4:0 d5:0 d6:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201202  U[u0:2 u1:2 u3:1 u7:1]  D[d2:1 d4:2 d5:0 d6:1 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202102  U[u0:2 u1:2 u3:1 u7:1]  D[d2:1 d4:1 d5:0 d6:2 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010210121  U[u0:2 u1:2 u3:0 u7:0]  D[d2:1 d4:2 d5:2 d6:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010210212  U[u0:2 u1:2 u3:0 u7:0]  D[d2:1 d4:2 d5:1 d6:0 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212012  U[u0:2 u1:2 u3:0 u7:0]  D[d2:1 d4:0 d5:1 d6:2 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212021  U[u0:2 u1:2 u3:0 u7:0]  D[d2:1 d4:0 d5:1 d6:1 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u3:0 u7:0]  D[d2:1 d4:0 d5:0 d6:0 d8:2]`
+
+## G19 — word=UUDUDDDUD bites=(6,8)
+
+1 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201202  U[u0:2 u1:2 u3:1 u7:1]  D[d2:1 d4:2 d5:0 p6_8:1]`
+
+## G20 — word=UUDUDDDUD bites=(2,8)
+
+6 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010120121  U[u0:2 u1:2 u3:0 u7:0]  D[d4:1 d5:2 d6:0 p2_8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121021  U[u0:2 u1:2 u3:0 u7:0]  D[d4:0 d5:2 d6:1 p2_8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010201202  U[u0:2 u1:2 u3:1 u7:1]  D[d4:2 d5:0 d6:1 p2_8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202102  U[u0:2 u1:2 u3:1 u7:1]  D[d4:1 d5:0 d6:2 p2_8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010210212  U[u0:2 u1:2 u3:0 u7:0]  D[d4:2 d5:1 d6:0 p2_8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212012  U[u0:2 u1:2 u3:0 u7:0]  D[d4:0 d5:1 d6:2 p2_8:1]`
+
+## G21 — word=UUDDUUDDD bites=-
+
+13 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010102012  U[u0:2 u1:2 u4:1 u5:1]  D[d2:2 d3:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010102021  U[u0:2 u1:2 u4:1 u5:1]  D[d2:2 d3:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120201  U[u0:2 u1:2 u4:1 u5:1]  D[d2:2 d3:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120202  U[u0:2 u1:2 u4:1 u5:1]  D[d2:2 d3:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120212  U[u0:2 u1:2 u4:1 u5:1]  D[d2:2 d3:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121201  U[u0:2 u1:2 u4:0 u5:0]  D[d2:2 d3:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121202  U[u0:2 u1:2 u4:0 u5:0]  D[d2:2 d3:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u4:0 u5:0]  D[d2:2 d3:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202012  U[u0:2 u1:2 u4:1 u5:1]  D[d2:1 d3:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u4:1 u5:1]  D[d2:1 d3:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212101  U[u0:2 u1:2 u4:0 u5:0]  D[d2:1 d3:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212102  U[u0:2 u1:2 u4:0 u5:0]  D[d2:1 d3:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u4:0 u5:0]  D[d2:1 d3:0 d6:0 d7:0 d8:2]`
+
+## G22 — word=UUDDUUDDD bites=(3,6)
+
+5 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010102012  U[u0:2 u1:2 u4:1 u5:1]  D[d2:2 d7:0 d8:1 p3_6:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120212  U[u0:2 u1:2 u4:1 u5:1]  D[d2:2 d7:0 d8:1 p3_6:0]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u4:0 u5:0]  D[d2:2 d7:0 d8:1 p3_6:0]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u4:1 u5:1]  D[d2:1 d7:0 d8:2 p3_6:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u4:0 u5:0]  D[d2:1 d7:0 d8:2 p3_6:0]`
+
+## G23 — word=UUDDUDUDD bites=-
+
+6 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010102021  U[u0:2 u1:2 u4:1 u6:1]  D[d2:2 d3:2 d5:1 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120201  U[u0:2 u1:2 u4:1 u6:1]  D[d2:2 d3:0 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120202  U[u0:2 u1:2 u4:1 u6:1]  D[d2:2 d3:0 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u4:0 u6:0]  D[d2:2 d3:0 d5:0 d7:0 d8:1]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010202021  U[u0:2 u1:2 u4:1 u6:1]  D[d2:1 d3:1 d5:1 d7:0 d8:2]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u4:0 u6:0]  D[d2:1 d3:0 d5:0 d7:0 d8:2]`
+
+## G24 — word=UUDDUDUDD bites=(5,7)
+
+3 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120202  U[u0:2 u1:2 u4:1 u6:1]  D[d2:2 d3:0 d8:1 p5_7:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u1:2 u4:0 u6:0]  D[d2:2 d3:0 d8:1 p5_7:0]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010212121  U[u0:2 u1:2 u4:0 u6:0]  D[d2:1 d3:0 d8:2 p5_7:0]`
+
+## G25 — word=UUDDUDUDD bites=(2,8)
+
+2 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010102021  U[u0:2 u1:2 u4:1 u6:1]  D[d3:2 d5:1 d7:0 p2_8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120201  U[u0:2 u1:2 u4:1 u6:1]  D[d3:0 d5:1 d7:2 p2_8:2]`
+
+## G26 — word=UDUDUDUDD bites=-
+
+4 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010102021  U[u0:2 u2:2 u4:1 u6:1]  D[d1:2 d3:2 d5:1 d7:0 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120201  U[u0:2 u2:2 u4:1 u6:1]  D[d1:2 d3:0 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120202  U[u0:2 u2:2 u4:1 u6:1]  D[d1:2 d3:0 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u2:2 u4:0 u6:0]  D[d1:2 d3:0 d5:0 d7:0 d8:1]`
+
+## G27 — word=UDUDUDUDD bites=(5,7)
+
+2 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2211` → canonical `0011`  ·  `A=010120202  U[u0:2 u2:2 u4:1 u6:1]  D[d1:2 d3:0 d8:1 p5_7:1]`
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u2:2 u4:0 u6:0]  D[d1:2 d3:0 d8:1 p5_7:0]`
+
+## G28 — word=UDUDUDUDD bites=(3,5)
+
+1 colouring(s) with up-tooth sequence `0011`:
+
+- up apexes (raw labels) `2200` → canonical `0011`  ·  `A=010121212  U[u0:2 u2:2 u4:0 u6:0]  D[d1:2 d7:0 d8:1 p3_5:0]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0011.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0011.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0011.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0011.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0101.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0101.md
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@@ -0,0 +1,150 @@
+# Up-tooth apex sequence `0101`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1.
+- Realised by **16** of 29 M(T) (dihedral classes).
+- **59** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_0101.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G08 — word=UUDUUDDDD bites=-
+
+5 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012012  U[u0:2 u1:0 u3:2 u4:0]  D[d2:1 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012021  U[u0:2 u1:0 u3:2 u4:0]  D[d2:1 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012101  U[u0:2 u1:0 u3:2 u4:0]  D[d2:1 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012102  U[u0:2 u1:0 u3:2 u4:0]  D[d2:1 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012121  U[u0:2 u1:0 u3:2 u4:0]  D[d2:1 d5:0 d6:0 d7:0 d8:2]`
+
+## G09 — word=UUDUUDDDD bites=(2,5)
+
+2 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012012  U[u0:2 u1:0 u3:2 u4:0]  D[d6:2 d7:0 d8:1 p2_5:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012021  U[u0:2 u1:0 u3:2 u4:0]  D[d6:1 d7:0 d8:2 p2_5:1]`
+
+## G10 — word=UUDUDUDDD bites=-
+
+9 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012101  U[u0:2 u1:0 u3:2 u5:0]  D[d2:1 d4:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012102  U[u0:2 u1:0 u3:2 u5:0]  D[d2:1 d4:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012121  U[u0:2 u1:0 u3:2 u5:0]  D[d2:1 d4:0 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101201  U[u0:2 u1:0 u3:2 u5:0]  D[d2:0 d4:2 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101202  U[u0:2 u1:0 u3:2 u5:0]  D[d2:0 d4:2 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u1:0 u3:2 u5:0]  D[d2:0 d4:2 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012102101  U[u0:2 u1:0 u3:2 u5:0]  D[d2:0 d4:1 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012102102  U[u0:2 u1:0 u3:2 u5:0]  D[d2:0 d4:1 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012102121  U[u0:2 u1:0 u3:2 u5:0]  D[d2:0 d4:1 d6:0 d7:0 d8:2]`
+
+## G11 — word=UUDUDUDDD bites=(4,6)
+
+1 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012121  U[u0:2 u1:0 u3:2 u5:0]  D[d2:1 d7:0 d8:2 p4_6:0]`
+
+## G13 — word=UUDUDUDDD bites=(2,8)
+
+1 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012102  U[u0:2 u1:0 u3:2 u5:0]  D[d4:0 d6:2 d7:1 p2_8:1]`
+
+## G14 — word=UUDUDDUDD bites=-
+
+5 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010121  U[u0:2 u1:0 u3:2 u6:0]  D[d2:1 d4:2 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010212  U[u0:2 u1:0 u3:2 u6:0]  D[d2:1 d4:2 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012121  U[u0:2 u1:0 u3:2 u6:0]  D[d2:1 d4:0 d5:0 d7:0 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u1:0 u3:2 u6:0]  D[d2:0 d4:2 d5:0 d7:0 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012102121  U[u0:2 u1:0 u3:2 u6:0]  D[d2:0 d4:1 d5:0 d7:0 d8:2]`
+
+## G15 — word=UUDUDDUDD bites=(5,7)
+
+3 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012121  U[u0:2 u1:0 u3:2 u6:0]  D[d2:1 d4:0 d8:2 p5_7:0]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u1:0 u3:2 u6:0]  D[d2:0 d4:2 d8:1 p5_7:0]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012102121  U[u0:2 u1:0 u3:2 u6:0]  D[d2:0 d4:1 d8:2 p5_7:0]`
+
+## G17 — word=UUDUDDUDD bites=(2,8)
+
+1 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010212  U[u0:2 u1:0 u3:2 u6:0]  D[d4:2 d5:1 d7:0 p2_8:1]`
+
+## G18 — word=UUDUDDDUD bites=-
+
+11 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010121  U[u0:2 u1:0 u3:2 u7:0]  D[d2:1 d4:2 d5:2 d6:0 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010212  U[u0:2 u1:0 u3:2 u7:0]  D[d2:1 d4:2 d5:1 d6:0 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012012  U[u0:2 u1:0 u3:2 u7:0]  D[d2:1 d4:0 d5:1 d6:2 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012021  U[u0:2 u1:0 u3:2 u7:0]  D[d2:1 d4:0 d5:1 d6:1 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012121  U[u0:2 u1:0 u3:2 u7:0]  D[d2:1 d4:0 d5:0 d6:0 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101012  U[u0:2 u1:0 u3:2 u7:0]  D[d2:0 d4:2 d5:2 d6:2 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101021  U[u0:2 u1:0 u3:2 u7:0]  D[d2:0 d4:2 d5:2 d6:1 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u1:0 u3:2 u7:0]  D[d2:0 d4:2 d5:0 d6:0 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012102012  U[u0:2 u1:0 u3:2 u7:0]  D[d2:0 d4:1 d5:1 d6:2 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012102021  U[u0:2 u1:0 u3:2 u7:0]  D[d2:0 d4:1 d5:1 d6:1 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012102121  U[u0:2 u1:0 u3:2 u7:0]  D[d2:0 d4:1 d5:0 d6:0 d8:2]`
+
+## G20 — word=UUDUDDDUD bites=(2,8)
+
+2 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010212  U[u0:2 u1:0 u3:2 u7:0]  D[d4:2 d5:1 d6:0 p2_8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012012012  U[u0:2 u1:0 u3:2 u7:0]  D[d4:0 d5:1 d6:2 p2_8:1]`
+
+## G21 — word=UUDDUUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101201  U[u0:2 u1:0 u4:2 u5:0]  D[d2:0 d3:2 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101202  U[u0:2 u1:0 u4:2 u5:0]  D[d2:0 d3:2 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u1:0 u4:2 u5:0]  D[d2:0 d3:2 d6:0 d7:0 d8:1]`
+
+## G23 — word=UUDDUDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010121  U[u0:2 u1:0 u4:2 u6:0]  D[d2:1 d3:2 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010212  U[u0:2 u1:0 u4:2 u6:0]  D[d2:1 d3:2 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u1:0 u4:2 u6:0]  D[d2:0 d3:2 d5:0 d7:0 d8:1]`
+
+## G24 — word=UUDDUDUDD bites=(5,7)
+
+1 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u1:0 u4:2 u6:0]  D[d2:0 d3:2 d8:1 p5_7:0]`
+
+## G25 — word=UUDDUDUDD bites=(2,8)
+
+1 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012010212  U[u0:2 u1:0 u4:2 u6:0]  D[d3:2 d5:1 d7:0 p2_8:1]`
+
+## G26 — word=UDUDUDUDD bites=-
+
+8 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=010201021  U[u0:2 u2:1 u4:2 u6:1]  D[d1:2 d3:1 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=010201201  U[u0:2 u2:1 u4:2 u6:1]  D[d1:2 d3:1 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=010201202  U[u0:2 u2:1 u4:2 u6:1]  D[d1:2 d3:1 d5:0 d7:1 d8:1]`
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=010210201  U[u0:2 u2:1 u4:2 u6:1]  D[d1:2 d3:0 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=010210202  U[u0:2 u2:1 u4:2 u6:1]  D[d1:2 d3:0 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=012010201  U[u0:2 u2:1 u4:2 u6:1]  D[d1:0 d3:2 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=012010202  U[u0:2 u2:1 u4:2 u6:1]  D[d1:0 d3:2 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u2:0 u4:2 u6:0]  D[d1:0 d3:2 d5:0 d7:0 d8:1]`
+
+## G27 — word=UDUDUDUDD bites=(5,7)
+
+3 colouring(s) with up-tooth sequence `0101`:
+
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=010210202  U[u0:2 u2:1 u4:2 u6:1]  D[d1:2 d3:0 d8:1 p5_7:1]`
+- up apexes (raw labels) `2121` → canonical `0101`  ·  `A=012010202  U[u0:2 u2:1 u4:2 u6:1]  D[d1:0 d3:2 d8:1 p5_7:1]`
+- up apexes (raw labels) `2020` → canonical `0101`  ·  `A=012101212  U[u0:2 u2:0 u4:2 u6:0]  D[d1:0 d3:2 d8:1 p5_7:0]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0101.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0101.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0101.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0101.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0110.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0110.md
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+# Up-tooth apex sequence `0110`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 4 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1.
+- Realised by **22** of 29 M(T) (dihedral classes).
+- **69** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_0110.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUDDDDD bites=-
+
+10 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u3:2]  D[d4:2 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101021  U[u0:2 u1:0 u2:0 u3:2]  D[d4:2 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101201  U[u0:2 u1:0 u2:0 u3:2]  D[d4:2 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101202  U[u0:2 u1:0 u2:0 u3:2]  D[d4:2 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101212  U[u0:2 u1:0 u2:0 u3:2]  D[d4:2 d5:0 d6:0 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012102012  U[u0:2 u1:0 u2:0 u3:2]  D[d4:1 d5:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012102021  U[u0:2 u1:0 u2:0 u3:2]  D[d4:1 d5:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012102101  U[u0:2 u1:0 u2:0 u3:2]  D[d4:1 d5:0 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012102102  U[u0:2 u1:0 u2:0 u3:2]  D[d4:1 d5:0 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012102121  U[u0:2 u1:0 u2:0 u3:2]  D[d4:1 d5:0 d6:0 d7:0 d8:2]`
+
+## G01 — word=UUUUDDDDD bites=(4,8)
+
+4 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101021  U[u0:2 u1:0 u2:0 u3:2]  D[d5:2 d6:1 d7:0 p4_8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101201  U[u0:2 u1:0 u2:0 u3:2]  D[d5:0 d6:1 d7:2 p4_8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012102012  U[u0:2 u1:0 u2:0 u3:2]  D[d5:1 d6:2 d7:0 p4_8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012102102  U[u0:2 u1:0 u2:0 u3:2]  D[d5:0 d6:2 d7:1 p4_8:1]`
+
+## G02 — word=UUUDUDDDD bites=-
+
+5 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u4:2]  D[d3:2 d5:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101021  U[u0:2 u1:0 u2:0 u4:2]  D[d3:2 d5:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101201  U[u0:2 u1:0 u2:0 u4:2]  D[d3:2 d5:0 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101202  U[u0:2 u1:0 u2:0 u4:2]  D[d3:2 d5:0 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101212  U[u0:2 u1:0 u2:0 u4:2]  D[d3:2 d5:0 d6:0 d7:0 d8:1]`
+
+## G03 — word=UUUDUDDDD bites=(3,5)
+
+2 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u4:2]  D[d6:2 d7:0 d8:1 p3_5:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101021  U[u0:2 u1:0 u2:0 u4:2]  D[d6:1 d7:0 d8:2 p3_5:2]`
+
+## G04 — word=UUUDUDDDD bites=(3,8)
+
+2 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101021  U[u0:2 u1:0 u2:0 u4:2]  D[d5:2 d6:1 d7:0 p3_8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101201  U[u0:2 u1:0 u2:0 u4:2]  D[d5:0 d6:1 d7:2 p3_8:2]`
+
+## G05 — word=UUUDDUDDD bites=-
+
+7 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u5:2]  D[d3:2 d4:2 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101021  U[u0:2 u1:0 u2:0 u5:2]  D[d3:2 d4:2 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120101  U[u0:2 u1:0 u2:0 u5:2]  D[d3:0 d4:1 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120102  U[u0:2 u1:0 u2:0 u5:2]  D[d3:0 d4:1 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120121  U[u0:2 u1:0 u2:0 u5:2]  D[d3:0 d4:1 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121012  U[u0:2 u1:0 u2:0 u5:2]  D[d3:0 d4:0 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121021  U[u0:2 u1:0 u2:0 u5:2]  D[d3:0 d4:0 d6:1 d7:0 d8:2]`
+
+## G06 — word=UUUDDUDDD bites=(4,6)
+
+1 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u5:2]  D[d3:2 d7:0 d8:1 p4_6:2]`
+
+## G07 — word=UUUDDUDDD bites=(3,8)
+
+1 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012101021  U[u0:2 u1:0 u2:0 u5:2]  D[d4:2 d6:1 d7:0 p3_8:2]`
+
+## G10 — word=UUDUDUDDD bites=-
+
+5 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120101  U[u0:2 u1:0 u3:0 u5:2]  D[d2:0 d4:1 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120102  U[u0:2 u1:0 u3:0 u5:2]  D[d2:0 d4:1 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120121  U[u0:2 u1:0 u3:0 u5:2]  D[d2:0 d4:1 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121012  U[u0:2 u1:0 u3:0 u5:2]  D[d2:0 d4:0 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121021  U[u0:2 u1:0 u3:0 u5:2]  D[d2:0 d4:0 d6:1 d7:0 d8:2]`
+
+## G12 — word=UUDUDUDDD bites=(2,4)
+
+2 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121012  U[u0:2 u1:0 u3:0 u5:2]  D[d6:2 d7:0 d8:1 p2_4:0]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121021  U[u0:2 u1:0 u3:0 u5:2]  D[d6:1 d7:0 d8:2 p2_4:0]`
+
+## G14 — word=UUDUDDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120101  U[u0:2 u1:0 u3:0 u6:2]  D[d2:0 d4:1 d5:2 d7:2 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120102  U[u0:2 u1:0 u3:0 u6:2]  D[d2:0 d4:1 d5:2 d7:1 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121012  U[u0:2 u1:0 u3:0 u6:2]  D[d2:0 d4:0 d5:2 d7:0 d8:1]`
+
+## G15 — word=UUDUDDUDD bites=(5,7)
+
+1 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120101  U[u0:2 u1:0 u3:0 u6:2]  D[d2:0 d4:1 d8:2 p5_7:2]`
+
+## G16 — word=UUDUDDUDD bites=(2,4)
+
+1 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121012  U[u0:2 u1:0 u3:0 u6:2]  D[d5:2 d7:0 d8:1 p2_4:0]`
+
+## G18 — word=UUDUDDDUD bites=-
+
+3 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120101  U[u0:2 u1:0 u3:0 u7:2]  D[d2:0 d4:1 d5:2 d6:2 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120201  U[u0:2 u1:0 u3:0 u7:2]  D[d2:0 d4:1 d5:1 d6:1 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121201  U[u0:2 u1:0 u3:0 u7:2]  D[d2:0 d4:0 d5:0 d6:1 d8:2]`
+
+## G19 — word=UUDUDDDUD bites=(6,8)
+
+1 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012120101  U[u0:2 u1:0 u3:0 u7:2]  D[d2:0 d4:1 d5:2 p6_8:2]`
+
+## G21 — word=UUDDUUDDD bites=-
+
+4 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012021012  U[u0:2 u1:0 u4:0 u5:2]  D[d2:1 d3:1 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012021021  U[u0:2 u1:0 u4:0 u5:2]  D[d2:1 d3:1 d6:1 d7:0 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121012  U[u0:2 u1:0 u4:0 u5:2]  D[d2:0 d3:0 d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121021  U[u0:2 u1:0 u4:0 u5:2]  D[d2:0 d3:0 d6:1 d7:0 d8:2]`
+
+## G22 — word=UUDDUUDDD bites=(3,6)
+
+1 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012021021  U[u0:2 u1:0 u4:0 u5:2]  D[d2:1 d7:0 d8:2 p3_6:1]`
+
+## G23 — word=UUDDUDUDD bites=-
+
+5 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012012012  U[u0:2 u1:0 u4:0 u6:2]  D[d2:1 d3:2 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012012101  U[u0:2 u1:0 u4:0 u6:2]  D[d2:1 d3:2 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012012102  U[u0:2 u1:0 u4:0 u6:2]  D[d2:1 d3:2 d5:0 d7:1 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012021012  U[u0:2 u1:0 u4:0 u6:2]  D[d2:1 d3:1 d5:2 d7:0 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121012  U[u0:2 u1:0 u4:0 u6:2]  D[d2:0 d3:0 d5:2 d7:0 d8:1]`
+
+## G25 — word=UUDDUDUDD bites=(2,8)
+
+3 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012012012  U[u0:2 u1:0 u4:0 u6:2]  D[d3:2 d5:1 d7:0 p2_8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012012102  U[u0:2 u1:0 u4:0 u6:2]  D[d3:2 d5:0 d7:1 p2_8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012021012  U[u0:2 u1:0 u4:0 u6:2]  D[d3:1 d5:2 d7:0 p2_8:1]`
+
+## G26 — word=UDUDUDUDD bites=-
+
+6 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2112` → canonical `0110`  ·  `A=010202012  U[u0:2 u2:1 u4:1 u6:2]  D[d1:2 d3:1 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `2112` → canonical `0110`  ·  `A=010202101  U[u0:2 u2:1 u4:1 u6:2]  D[d1:2 d3:1 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `2112` → canonical `0110`  ·  `A=010202102  U[u0:2 u2:1 u4:1 u6:2]  D[d1:2 d3:1 d5:0 d7:1 d8:1]`
+- up apexes (raw labels) `2112` → canonical `0110`  ·  `A=012020101  U[u0:2 u2:1 u4:1 u6:2]  D[d1:0 d3:1 d5:2 d7:2 d8:2]`
+- up apexes (raw labels) `2112` → canonical `0110`  ·  `A=012020102  U[u0:2 u2:1 u4:1 u6:2]  D[d1:0 d3:1 d5:2 d7:1 d8:1]`
+- up apexes (raw labels) `2002` → canonical `0110`  ·  `A=012121012  U[u0:2 u2:0 u4:0 u6:2]  D[d1:0 d3:0 d5:2 d7:0 d8:1]`
+
+## G27 — word=UDUDUDUDD bites=(5,7)
+
+1 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2112` → canonical `0110`  ·  `A=012020101  U[u0:2 u2:1 u4:1 u6:2]  D[d1:0 d3:1 d8:2 p5_7:2]`
+
+## G28 — word=UDUDUDUDD bites=(3,5)
+
+1 colouring(s) with up-tooth sequence `0110`:
+
+- up apexes (raw labels) `2112` → canonical `0110`  ·  `A=010202012  U[u0:2 u2:1 u4:1 u6:2]  D[d1:2 d7:0 d8:1 p3_5:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0110.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/seq_0110.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/summary.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m4/summary.md
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+# Up-tooth apex sequences of Kempe-balanced colourings (n=9, m=4)
+
+Every full medial tire graph M(T) with |A(T)| = 9 and exactly 4 up teeth, one representative per dihedral class: **29 M(T)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the up-tooth apex colour sequence u0<u1<... in cyclic order, and reduce it modulo colour permutation (NOT dihedral symmetry).
+
+- Total Kempe-balanced colourings (mod colour permutation): **343**.
+- Distinct canonical up-tooth sequences overall: **4**.
+
+## Distinct canonical up-tooth sequences
+
+| sequence | colour multiset | #M(T) realising | #colourings |
+|---|---|---|---|
+| `0000` | 4 | 27 | 75 |
+| `0011` | 2+2 | 29 | 140 |
+| `0101` | 2+2 | 16 | 59 |
+| `0110` | 2+2 | 22 | 69 |
+
+Note: every realised sequence has its three colour-counts of **equal parity** — exactly the outer-face Kempe-parity constraint (each colour pair meets the up-tooth apexes an even number of times). With m = 4 up teeth (m is even) every count must be **even**, so the only admissible colour multisets are 2+2, 4.
+
+## Step 4 — grouping M(T) by their set of unique up-tooth sequences
+
+The 29 M(T) fall into **4** groups by the set of canonical up-tooth sequences they realise:
+
+| #M(T) | set of up-tooth sequences | M(T) ids |
+|---|---|---|
+| 13 | { `0000`, `0011`, `0110` } | G00, G01, G02, G03, G04, G05, G06, G07, G12, G16, G19, G22, G28 |
+| 7 | { `0000`, `0011`, `0101` } | G08, G09, G11, G13, G17, G20, G24 |
+| 7 | { `0000`, `0011`, `0101`, `0110` } | G10, G14, G18, G21, G23, G25, G26 |
+| 2 | { `0011`, `0101`, `0110` } | G15, G27 |
+
+## M(T) atlas (ids)
+
+| id | word / bites | #Kempe-balanced | up-tooth sequence set |
+|---|---|---|---|
+| G00 | word=UUUUDDDDD bites=- | 30 | { `0000`, `0011`, `0110` } |
+| G01 | word=UUUUDDDDD bites=(4,8) | 12 | { `0000`, `0011`, `0110` } |
+| G02 | word=UUUDUDDDD bites=- | 15 | { `0000`, `0011`, `0110` } |
+| G03 | word=UUUDUDDDD bites=(3,5) | 6 | { `0000`, `0011`, `0110` } |
+| G04 | word=UUUDUDDDD bites=(3,8) | 6 | { `0000`, `0011`, `0110` } |
+| G05 | word=UUUDDUDDD bites=- | 21 | { `0000`, `0011`, `0110` } |
+| G06 | word=UUUDDUDDD bites=(4,6) | 3 | { `0000`, `0011`, `0110` } |
+| G07 | word=UUUDDUDDD bites=(3,8) | 3 | { `0000`, `0011`, `0110` } |
+| G08 | word=UUDUUDDDD bites=- | 25 | { `0000`, `0011`, `0101` } |
+| G09 | word=UUDUUDDDD bites=(2,5) | 10 | { `0000`, `0011`, `0101` } |
+| G10 | word=UUDUDUDDD bites=- | 24 | { `0000`, `0011`, `0101`, `0110` } |
+| G11 | word=UUDUDUDDD bites=(4,6) | 5 | { `0000`, `0011`, `0101` } |
+| G12 | word=UUDUDUDDD bites=(2,4) | 6 | { `0000`, `0011`, `0110` } |
+| G13 | word=UUDUDUDDD bites=(2,8) | 5 | { `0000`, `0011`, `0101` } |
+| G14 | word=UUDUDDUDD bites=- | 22 | { `0000`, `0011`, `0101`, `0110` } |
+| G15 | word=UUDUDDUDD bites=(5,7) | 6 | { `0011`, `0101`, `0110` } |
+| G16 | word=UUDUDDUDD bites=(2,4) | 3 | { `0000`, `0011`, `0110` } |
+| G17 | word=UUDUDDUDD bites=(2,8) | 5 | { `0000`, `0011`, `0101` } |
+| G18 | word=UUDUDDDUD bites=- | 28 | { `0000`, `0011`, `0101`, `0110` } |
+| G19 | word=UUDUDDDUD bites=(6,8) | 3 | { `0000`, `0011`, `0110` } |
+| G20 | word=UUDUDDDUD bites=(2,8) | 10 | { `0000`, `0011`, `0101` } |
+| G21 | word=UUDDUUDDD bites=- | 27 | { `0000`, `0011`, `0101`, `0110` } |
+| G22 | word=UUDDUUDDD bites=(3,6) | 9 | { `0000`, `0011`, `0110` } |
+| G23 | word=UUDDUDUDD bites=- | 18 | { `0000`, `0011`, `0101`, `0110` } |
+| G24 | word=UUDDUDUDD bites=(5,7) | 5 | { `0000`, `0011`, `0101` } |
+| G25 | word=UUDDUDUDD bites=(2,8) | 8 | { `0000`, `0011`, `0101`, `0110` } |
+| G26 | word=UDUDUDUDD bites=- | 19 | { `0000`, `0011`, `0101`, `0110` } |
+| G27 | word=UDUDUDUDD bites=(5,7) | 6 | { `0011`, `0101`, `0110` } |
+| G28 | word=UDUDUDUDD bites=(3,5) | 3 | { `0000`, `0011`, `0110` } |
+
+## Per-sequence notes
+
+- [`0000`](seq_0000.md) — figure `seq_0000.png`
+- [`0011`](seq_0011.md) — figure `seq_0011.png`
+- [`0101`](seq_0101.md) — figure `seq_0101.png`
+- [`0110`](seq_0110.md) — figure `seq_0110.png`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00012.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00012.md
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+# Up-tooth apex sequence `00012`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
+- Realised by **18** of 18 M(T) (dihedral classes).
+- **49** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_00012.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUDDDD bites=-
+
+6 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120101  U[u0:2 u1:2 u2:2 u3:0 u4:1]  D[d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120102  U[u0:2 u1:2 u2:2 u3:0 u4:1]  D[d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120121  U[u0:2 u1:2 u2:2 u3:0 u4:1]  D[d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120201  U[u0:2 u1:2 u2:2 u3:0 u4:1]  D[d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120202  U[u0:2 u1:2 u2:2 u3:0 u4:1]  D[d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120212  U[u0:2 u1:2 u2:2 u3:0 u4:1]  D[d5:1 d6:0 d7:0 d8:1]`
+
+## G01 — word=UUUUDUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120201  U[u0:2 u1:2 u2:2 u3:0 u5:1]  D[d4:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120202  U[u0:2 u1:2 u2:2 u3:0 u5:1]  D[d4:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120212  U[u0:2 u1:2 u2:2 u3:0 u5:1]  D[d4:1 d6:0 d7:0 d8:1]`
+
+## G02 — word=UUUUDDUDD bites=-
+
+5 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120201  U[u0:2 u1:2 u2:2 u3:0 u6:1]  D[d4:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120202  U[u0:2 u1:2 u2:2 u3:0 u6:1]  D[d4:1 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121021  U[u0:2 u1:2 u2:2 u3:0 u6:1]  D[d4:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121201  U[u0:2 u1:2 u2:2 u3:0 u6:1]  D[d4:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121202  U[u0:2 u1:2 u2:2 u3:0 u6:1]  D[d4:0 d5:0 d7:1 d8:1]`
+
+## G03 — word=UUUUDDUDD bites=(4,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010120202  U[u0:2 u1:2 u2:2 u3:0 u6:1]  D[p4_8:1 p5_7:1]`
+
+## G04 — word=UUUDUUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102101  U[u0:2 u1:2 u2:2 u4:1 u5:0]  D[d3:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102102  U[u0:2 u1:2 u2:2 u4:1 u5:0]  D[d3:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102121  U[u0:2 u1:2 u2:2 u4:1 u5:0]  D[d3:2 d6:0 d7:0 d8:2]`
+
+## G05 — word=UUUDUDUDD bites=-
+
+6 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102121  U[u0:2 u1:2 u2:2 u4:1 u6:0]  D[d3:2 d5:0 d7:0 d8:2]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010120121  U[u0:2 u1:2 u2:2 u4:1 u6:0]  D[d3:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010120212  U[u0:2 u1:2 u2:2 u4:1 u6:0]  D[d3:0 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121021  U[u0:2 u1:2 u2:2 u4:0 u6:1]  D[d3:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121201  U[u0:2 u1:2 u2:2 u4:0 u6:1]  D[d3:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121202  U[u0:2 u1:2 u2:2 u4:0 u6:1]  D[d3:0 d5:0 d7:1 d8:1]`
+
+## G06 — word=UUUDUDUDD bites=(3,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102121  U[u0:2 u1:2 u2:2 u4:1 u6:0]  D[p3_8:2 p5_7:0]`
+
+## G07 — word=UUUDUDDUD bites=-
+
+6 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102012  U[u0:2 u1:2 u2:2 u4:1 u7:0]  D[d3:2 d5:1 d6:2 d8:1]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102021  U[u0:2 u1:2 u2:2 u4:1 u7:0]  D[d3:2 d5:1 d6:1 d8:2]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102121  U[u0:2 u1:2 u2:2 u4:1 u7:0]  D[d3:2 d5:0 d6:0 d8:2]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010120121  U[u0:2 u1:2 u2:2 u4:1 u7:0]  D[d3:0 d5:2 d6:0 d8:2]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010120212  U[u0:2 u1:2 u2:2 u4:1 u7:0]  D[d3:0 d5:1 d6:0 d8:1]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121202  U[u0:2 u1:2 u2:2 u4:0 u7:1]  D[d3:0 d5:0 d6:1 d8:1]`
+
+## G08 — word=UUUDUDDUD bites=(3,5),(6,8)
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121202  U[u0:2 u1:2 u2:2 u4:0 u7:1]  D[p3_5:0 p6_8:1]`
+
+## G09 — word=UUUDDUUDD bites=-
+
+5 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010101201  U[u0:2 u1:2 u2:2 u5:0 u6:1]  D[d3:2 d4:2 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010101202  U[u0:2 u1:2 u2:2 u5:0 u6:1]  D[d3:2 d4:2 d7:1 d8:1]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010120212  U[u0:2 u1:2 u2:2 u5:1 u6:0]  D[d3:0 d4:1 d7:0 d8:1]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121201  U[u0:2 u1:2 u2:2 u5:0 u6:1]  D[d3:0 d4:0 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010121202  U[u0:2 u1:2 u2:2 u5:0 u6:1]  D[d3:0 d4:0 d7:1 d8:1]`
+
+## G10 — word=UUUDDUUDD bites=(3,8),(4,7)
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010101201  U[u0:2 u1:2 u2:2 u5:0 u6:1]  D[p3_8:2 p4_7:2]`
+
+## G11 — word=UUDUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102121  U[u0:2 u1:2 u3:2 u4:1 u6:0]  D[d2:2 d5:0 d7:0 d8:2]`
+
+## G12 — word=UUDUUDUDD bites=(2,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102121  U[u0:2 u1:2 u3:2 u4:1 u6:0]  D[p2_8:2 p5_7:0]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+2 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010101201  U[u0:2 u1:2 u3:2 u5:0 u6:1]  D[d2:2 d4:2 d7:2 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010101202  U[u0:2 u1:2 u3:2 u5:0 u6:1]  D[d2:2 d4:2 d7:1 d8:1]`
+
+## G14 — word=UUDUDUUDD bites=(2,8),(4,7)
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010101201  U[u0:2 u1:2 u3:2 u5:0 u6:1]  D[p2_8:2 p4_7:2]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+4 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010101202  U[u0:2 u1:2 u3:2 u5:0 u7:1]  D[d2:2 d4:2 d6:1 d8:1]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102012  U[u0:2 u1:2 u3:2 u5:1 u7:0]  D[d2:2 d4:1 d6:2 d8:1]`
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102021  U[u0:2 u1:2 u3:2 u5:1 u7:0]  D[d2:2 d4:1 d6:1 d8:2]`
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010102102  U[u0:2 u1:2 u3:2 u5:0 u7:1]  D[d2:2 d4:1 d6:2 d8:1]`
+
+## G16 — word=UUDUDUDUD bites=(2,4),(6,8)
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22201` → canonical `00012`  ·  `A=010101202  U[u0:2 u1:2 u3:2 u5:0 u7:1]  D[p2_4:2 p6_8:1]`
+
+## G17 — word=UUDUDUDUD bites=(2,8),(4,6)
+
+1 colouring(s) with up-tooth sequence `00012`:
+
+- up apexes (raw labels) `22210` → canonical `00012`  ·  `A=010102021  U[u0:2 u1:2 u3:2 u5:1 u7:0]  D[p2_8:2 p4_6:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00012.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00012.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00102.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00102.md
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@@ -0,0 +1,92 @@
+# Up-tooth apex sequence `00102`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
+- Realised by **11** of 18 M(T) (dihedral classes).
+- **26** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_00102.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G04 — word=UUUDUUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201201  U[u0:2 u1:2 u2:1 u4:2 u5:0]  D[d3:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201202  U[u0:2 u1:2 u2:1 u4:2 u5:0]  D[d3:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201212  U[u0:2 u1:2 u2:1 u4:2 u5:0]  D[d3:1 d6:0 d7:0 d8:1]`
+
+## G05 — word=UUUDUDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201212  U[u0:2 u1:2 u2:1 u4:2 u6:0]  D[d3:1 d5:0 d7:0 d8:1]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010210121  U[u0:2 u1:2 u2:1 u4:2 u6:0]  D[d3:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010210212  U[u0:2 u1:2 u2:1 u4:2 u6:0]  D[d3:0 d5:1 d7:0 d8:1]`
+
+## G06 — word=UUUDUDUDD bites=(3,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201212  U[u0:2 u1:2 u2:1 u4:2 u6:0]  D[p3_8:1 p5_7:0]`
+
+## G07 — word=UUUDUDDUD bites=-
+
+5 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201012  U[u0:2 u1:2 u2:1 u4:2 u7:0]  D[d3:1 d5:2 d6:2 d8:1]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201021  U[u0:2 u1:2 u2:1 u4:2 u7:0]  D[d3:1 d5:2 d6:1 d8:2]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201212  U[u0:2 u1:2 u2:1 u4:2 u7:0]  D[d3:1 d5:0 d6:0 d8:1]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010210121  U[u0:2 u1:2 u2:1 u4:2 u7:0]  D[d3:0 d5:2 d6:0 d8:2]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010210212  U[u0:2 u1:2 u2:1 u4:2 u7:0]  D[d3:0 d5:1 d6:0 d8:1]`
+
+## G09 — word=UUUDDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010210121  U[u0:2 u1:2 u2:1 u5:2 u6:0]  D[d3:0 d4:2 d7:0 d8:2]`
+
+## G11 — word=UUDUUDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201212  U[u0:2 u1:2 u3:1 u4:2 u6:0]  D[d2:1 d5:0 d7:0 d8:1]`
+- up apexes (raw labels) `22021` → canonical `00102`  ·  `A=010210201  U[u0:2 u1:2 u3:0 u4:2 u6:1]  D[d2:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `22021` → canonical `00102`  ·  `A=010210202  U[u0:2 u1:2 u3:0 u4:2 u6:1]  D[d2:1 d5:1 d7:1 d8:1]`
+
+## G12 — word=UUDUUDUDD bites=(2,8),(5,7)
+
+2 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201212  U[u0:2 u1:2 u3:1 u4:2 u6:0]  D[p2_8:1 p5_7:0]`
+- up apexes (raw labels) `22021` → canonical `00102`  ·  `A=010210202  U[u0:2 u1:2 u3:0 u4:2 u6:1]  D[p2_8:1 p5_7:1]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22021` → canonical `00102`  ·  `A=010121021  U[u0:2 u1:2 u3:0 u5:2 u6:1]  D[d2:2 d4:0 d7:0 d8:2]`
+
+## G14 — word=UUDUDUUDD bites=(2,8),(4,7)
+
+1 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22021` → canonical `00102`  ·  `A=010121021  U[u0:2 u1:2 u3:0 u5:2 u6:1]  D[p2_8:2 p4_7:0]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+4 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22021` → canonical `00102`  ·  `A=010120102  U[u0:2 u1:2 u3:0 u5:2 u7:1]  D[d2:2 d4:1 d6:2 d8:1]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201012  U[u0:2 u1:2 u3:1 u5:2 u7:0]  D[d2:1 d4:2 d6:2 d8:1]`
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201021  U[u0:2 u1:2 u3:1 u5:2 u7:0]  D[d2:1 d4:2 d6:1 d8:2]`
+- up apexes (raw labels) `22021` → canonical `00102`  ·  `A=010210102  U[u0:2 u1:2 u3:0 u5:2 u7:1]  D[d2:1 d4:2 d6:2 d8:1]`
+
+## G17 — word=UUDUDUDUD bites=(2,8),(4,6)
+
+2 colouring(s) with up-tooth sequence `00102`:
+
+- up apexes (raw labels) `22120` → canonical `00102`  ·  `A=010201012  U[u0:2 u1:2 u3:1 u5:2 u7:0]  D[p2_8:1 p4_6:2]`
+- up apexes (raw labels) `22021` → canonical `00102`  ·  `A=010210102  U[u0:2 u1:2 u3:0 u5:2 u7:1]  D[p2_8:1 p4_6:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00102.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00102.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00102.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00102.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00120.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00120.md
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@@ -0,0 +1,130 @@
+# Up-tooth apex sequence `00120`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
+- Realised by **16** of 18 M(T) (dihedral classes).
+- **39** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_00120.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUDDDD bites=-
+
+6 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210101  U[u0:2 u1:2 u2:1 u3:0 u4:2]  D[d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210102  U[u0:2 u1:2 u2:1 u3:0 u4:2]  D[d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210121  U[u0:2 u1:2 u2:1 u3:0 u4:2]  D[d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210201  U[u0:2 u1:2 u2:1 u3:0 u4:2]  D[d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210202  U[u0:2 u1:2 u2:1 u3:0 u4:2]  D[d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210212  U[u0:2 u1:2 u2:1 u3:0 u4:2]  D[d5:1 d6:0 d7:0 d8:1]`
+
+## G01 — word=UUUUDUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210101  U[u0:2 u1:2 u2:1 u3:0 u5:2]  D[d4:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210102  U[u0:2 u1:2 u2:1 u3:0 u5:2]  D[d4:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210121  U[u0:2 u1:2 u2:1 u3:0 u5:2]  D[d4:2 d6:0 d7:0 d8:2]`
+
+## G02 — word=UUUUDDUDD bites=-
+
+5 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210101  U[u0:2 u1:2 u2:1 u3:0 u6:2]  D[d4:2 d5:2 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210102  U[u0:2 u1:2 u2:1 u3:0 u6:2]  D[d4:2 d5:2 d7:1 d8:1]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212012  U[u0:2 u1:2 u2:1 u3:0 u6:2]  D[d4:0 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212101  U[u0:2 u1:2 u2:1 u3:0 u6:2]  D[d4:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212102  U[u0:2 u1:2 u2:1 u3:0 u6:2]  D[d4:0 d5:0 d7:1 d8:1]`
+
+## G03 — word=UUUUDDUDD bites=(4,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010210101  U[u0:2 u1:2 u2:1 u3:0 u6:2]  D[p4_8:2 p5_7:2]`
+
+## G05 — word=UUUDUDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212012  U[u0:2 u1:2 u2:1 u4:0 u6:2]  D[d3:0 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212101  U[u0:2 u1:2 u2:1 u4:0 u6:2]  D[d3:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212102  U[u0:2 u1:2 u2:1 u4:0 u6:2]  D[d3:0 d5:0 d7:1 d8:1]`
+
+## G07 — word=UUUDUDDUD bites=-
+
+1 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212101  U[u0:2 u1:2 u2:1 u4:0 u7:2]  D[d3:0 d5:0 d6:2 d8:2]`
+
+## G08 — word=UUUDUDDUD bites=(3,5),(6,8)
+
+1 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212101  U[u0:2 u1:2 u2:1 u4:0 u7:2]  D[p3_5:0 p6_8:2]`
+
+## G09 — word=UUUDDUUDD bites=-
+
+4 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010202101  U[u0:2 u1:2 u2:1 u5:0 u6:2]  D[d3:1 d4:1 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010202102  U[u0:2 u1:2 u2:1 u5:0 u6:2]  D[d3:1 d4:1 d7:1 d8:1]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212101  U[u0:2 u1:2 u2:1 u5:0 u6:2]  D[d3:0 d4:0 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010212102  U[u0:2 u1:2 u2:1 u5:0 u6:2]  D[d3:0 d4:0 d7:1 d8:1]`
+
+## G10 — word=UUUDDUUDD bites=(3,8),(4,7)
+
+1 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010202102  U[u0:2 u1:2 u2:1 u5:0 u6:2]  D[p3_8:1 p4_7:1]`
+
+## G11 — word=UUDUUDUDD bites=-
+
+2 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22012` → canonical `00120`  ·  `A=010120101  U[u0:2 u1:2 u3:0 u4:1 u6:2]  D[d2:2 d5:2 d7:2 d8:2]`
+- up apexes (raw labels) `22012` → canonical `00120`  ·  `A=010120102  U[u0:2 u1:2 u3:0 u4:1 u6:2]  D[d2:2 d5:2 d7:1 d8:1]`
+
+## G12 — word=UUDUUDUDD bites=(2,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22012` → canonical `00120`  ·  `A=010120101  U[u0:2 u1:2 u3:0 u4:1 u6:2]  D[p2_8:2 p5_7:2]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+3 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010202101  U[u0:2 u1:2 u3:1 u5:0 u6:2]  D[d2:1 d4:1 d7:2 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010202102  U[u0:2 u1:2 u3:1 u5:0 u6:2]  D[d2:1 d4:1 d7:1 d8:1]`
+- up apexes (raw labels) `22012` → canonical `00120`  ·  `A=010212012  U[u0:2 u1:2 u3:0 u5:1 u6:2]  D[d2:1 d4:0 d7:0 d8:1]`
+
+## G14 — word=UUDUDUUDD bites=(2,8),(4,7)
+
+2 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010202102  U[u0:2 u1:2 u3:1 u5:0 u6:2]  D[p2_8:1 p4_7:1]`
+- up apexes (raw labels) `22012` → canonical `00120`  ·  `A=010212012  U[u0:2 u1:2 u3:0 u5:1 u6:2]  D[p2_8:1 p4_7:0]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+4 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22012` → canonical `00120`  ·  `A=010120201  U[u0:2 u1:2 u3:0 u5:1 u7:2]  D[d2:2 d4:1 d6:1 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010201201  U[u0:2 u1:2 u3:1 u5:0 u7:2]  D[d2:1 d4:2 d6:1 d8:2]`
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010202101  U[u0:2 u1:2 u3:1 u5:0 u7:2]  D[d2:1 d4:1 d6:2 d8:2]`
+- up apexes (raw labels) `22012` → canonical `00120`  ·  `A=010210201  U[u0:2 u1:2 u3:0 u5:1 u7:2]  D[d2:1 d4:2 d6:1 d8:2]`
+
+## G16 — word=UUDUDUDUD bites=(2,4),(6,8)
+
+1 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22102` → canonical `00120`  ·  `A=010202101  U[u0:2 u1:2 u3:1 u5:0 u7:2]  D[p2_4:1 p6_8:2]`
+
+## G17 — word=UUDUDUDUD bites=(2,8),(4,6)
+
+1 colouring(s) with up-tooth sequence `00120`:
+
+- up apexes (raw labels) `22012` → canonical `00120`  ·  `A=010120201  U[u0:2 u1:2 u3:0 u5:1 u7:2]  D[p2_8:2 p4_6:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00120.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00120.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00120.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_00120.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01002.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01002.md
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@@ -0,0 +1,45 @@
+# Up-tooth apex sequence `01002`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
+- Realised by **5** of 18 M(T) (dihedral classes).
+- **9** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_01002.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G11 — word=UUDUUDUDD bites=-
+
+5 colouring(s) with up-tooth sequence `01002`:
+
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012010201  U[u0:2 u1:0 u3:2 u4:2 u6:1]  D[d2:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012010202  U[u0:2 u1:0 u3:2 u4:2 u6:1]  D[d2:1 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012101021  U[u0:2 u1:0 u3:2 u4:2 u6:1]  D[d2:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012101201  U[u0:2 u1:0 u3:2 u4:2 u6:1]  D[d2:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012101202  U[u0:2 u1:0 u3:2 u4:2 u6:1]  D[d2:0 d5:0 d7:1 d8:1]`
+
+## G12 — word=UUDUUDUDD bites=(2,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01002`:
+
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012010202  U[u0:2 u1:0 u3:2 u4:2 u6:1]  D[p2_8:1 p5_7:1]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `01002`:
+
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012101021  U[u0:2 u1:0 u3:2 u5:2 u6:1]  D[d2:0 d4:2 d7:0 d8:2]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `01002`:
+
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012010102  U[u0:2 u1:0 u3:2 u5:2 u7:1]  D[d2:1 d4:2 d6:2 d8:1]`
+
+## G17 — word=UUDUDUDUD bites=(2,8),(4,6)
+
+1 colouring(s) with up-tooth sequence `01002`:
+
+- up apexes (raw labels) `20221` → canonical `01002`  ·  `A=012010102  U[u0:2 u1:0 u3:2 u5:2 u7:1]  D[p2_8:1 p4_6:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01002.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01002.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01002.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01002.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01020.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01020.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01020.md
@@ -0,0 +1,38 @@
+# Up-tooth apex sequence `01020`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
+- Realised by **4** of 18 M(T) (dihedral classes).
+- **7** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_01020.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G11 — word=UUDUUDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `01020`:
+
+- up apexes (raw labels) `20212` → canonical `01020`  ·  `A=012102012  U[u0:2 u1:0 u3:2 u4:1 u6:2]  D[d2:0 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `20212` → canonical `01020`  ·  `A=012102101  U[u0:2 u1:0 u3:2 u4:1 u6:2]  D[d2:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `20212` → canonical `01020`  ·  `A=012102102  U[u0:2 u1:0 u3:2 u4:1 u6:2]  D[d2:0 d5:0 d7:1 d8:1]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01020`:
+
+- up apexes (raw labels) `20212` → canonical `01020`  ·  `A=012012012  U[u0:2 u1:0 u3:2 u5:1 u6:2]  D[d2:1 d4:0 d7:0 d8:1]`
+- up apexes (raw labels) `20212` → canonical `01020`  ·  `A=012102012  U[u0:2 u1:0 u3:2 u5:1 u6:2]  D[d2:0 d4:1 d7:0 d8:1]`
+
+## G14 — word=UUDUDUUDD bites=(2,8),(4,7)
+
+1 colouring(s) with up-tooth sequence `01020`:
+
+- up apexes (raw labels) `20212` → canonical `01020`  ·  `A=012012012  U[u0:2 u1:0 u3:2 u5:1 u6:2]  D[p2_8:1 p4_7:0]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `01020`:
+
+- up apexes (raw labels) `20212` → canonical `01020`  ·  `A=012010201  U[u0:2 u1:0 u3:2 u5:1 u7:2]  D[d2:1 d4:2 d6:1 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01020.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01020.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01020.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01020.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01112.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01112.md
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--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01112.md
@@ -0,0 +1,108 @@
+# Up-tooth apex sequence `01112`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 1×colour0, 3×colour1, 1×colour2.
+- Realised by **13** of 18 M(T) (dihedral classes).
+- **32** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_01112.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUDDDD bites=-
+
+6 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120101  U[u0:2 u1:0 u2:0 u3:0 u4:1]  D[d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120102  U[u0:2 u1:0 u2:0 u3:0 u4:1]  D[d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120121  U[u0:2 u1:0 u2:0 u3:0 u4:1]  D[d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120201  U[u0:2 u1:0 u2:0 u3:0 u4:1]  D[d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120202  U[u0:2 u1:0 u2:0 u3:0 u4:1]  D[d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120212  U[u0:2 u1:0 u2:0 u3:0 u4:1]  D[d5:1 d6:0 d7:0 d8:1]`
+
+## G01 — word=UUUUDUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120201  U[u0:2 u1:0 u2:0 u3:0 u5:1]  D[d4:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120202  U[u0:2 u1:0 u2:0 u3:0 u5:1]  D[d4:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120212  U[u0:2 u1:0 u2:0 u3:0 u5:1]  D[d4:1 d6:0 d7:0 d8:1]`
+
+## G02 — word=UUUUDDUDD bites=-
+
+5 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120201  U[u0:2 u1:0 u2:0 u3:0 u6:1]  D[d4:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120202  U[u0:2 u1:0 u2:0 u3:0 u6:1]  D[d4:1 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121021  U[u0:2 u1:0 u2:0 u3:0 u6:1]  D[d4:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121201  U[u0:2 u1:0 u2:0 u3:0 u6:1]  D[d4:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u2:0 u3:0 u6:1]  D[d4:0 d5:0 d7:1 d8:1]`
+
+## G03 — word=UUUUDDUDD bites=(4,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012120202  U[u0:2 u1:0 u2:0 u3:0 u6:1]  D[p4_8:1 p5_7:1]`
+
+## G05 — word=UUUDUDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121021  U[u0:2 u1:0 u2:0 u4:0 u6:1]  D[d3:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121201  U[u0:2 u1:0 u2:0 u4:0 u6:1]  D[d3:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u2:0 u4:0 u6:1]  D[d3:0 d5:0 d7:1 d8:1]`
+
+## G07 — word=UUUDUDDUD bites=-
+
+1 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u2:0 u4:0 u7:1]  D[d3:0 d5:0 d6:1 d8:1]`
+
+## G08 — word=UUUDUDDUD bites=(3,5),(6,8)
+
+1 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u2:0 u4:0 u7:1]  D[p3_5:0 p6_8:1]`
+
+## G09 — word=UUUDDUUDD bites=-
+
+4 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012101201  U[u0:2 u1:0 u2:0 u5:0 u6:1]  D[d3:2 d4:2 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012101202  U[u0:2 u1:0 u2:0 u5:0 u6:1]  D[d3:2 d4:2 d7:1 d8:1]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121201  U[u0:2 u1:0 u2:0 u5:0 u6:1]  D[d3:0 d4:0 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u2:0 u5:0 u6:1]  D[d3:0 d4:0 d7:1 d8:1]`
+
+## G10 — word=UUUDDUUDD bites=(3,8),(4,7)
+
+1 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012101201  U[u0:2 u1:0 u2:0 u5:0 u6:1]  D[p3_8:2 p4_7:2]`
+
+## G11 — word=UUDUUDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121021  U[u0:2 u1:0 u3:0 u4:0 u6:1]  D[d2:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121201  U[u0:2 u1:0 u3:0 u4:0 u6:1]  D[d2:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u3:0 u4:0 u6:1]  D[d2:0 d5:0 d7:1 d8:1]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121201  U[u0:2 u1:0 u3:0 u5:0 u6:1]  D[d2:0 d4:0 d7:2 d8:2]`
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u3:0 u5:0 u6:1]  D[d2:0 d4:0 d7:1 d8:1]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u3:0 u5:0 u7:1]  D[d2:0 d4:0 d6:1 d8:1]`
+
+## G16 — word=UUDUDUDUD bites=(2,4),(6,8)
+
+1 colouring(s) with up-tooth sequence `01112`:
+
+- up apexes (raw labels) `20001` → canonical `01112`  ·  `A=012121202  U[u0:2 u1:0 u3:0 u5:0 u7:1]  D[p2_4:0 p6_8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01112.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01112.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01112.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01112.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01121.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01121.md
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@@ -0,0 +1,68 @@
+# Up-tooth apex sequence `01121`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 1×colour0, 3×colour1, 1×colour2.
+- Realised by **8** of 18 M(T) (dihedral classes).
+- **17** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_01121.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G04 — word=UUUDUUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `01121`:
+
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012102101  U[u0:2 u1:0 u2:0 u4:1 u5:0]  D[d3:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012102102  U[u0:2 u1:0 u2:0 u4:1 u5:0]  D[d3:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012102121  U[u0:2 u1:0 u2:0 u4:1 u5:0]  D[d3:2 d6:0 d7:0 d8:2]`
+
+## G05 — word=UUUDUDUDD bites=-
+
+3 colouring(s) with up-tooth sequence `01121`:
+
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012102121  U[u0:2 u1:0 u2:0 u4:1 u6:0]  D[d3:2 d5:0 d7:0 d8:2]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120121  U[u0:2 u1:0 u2:0 u4:1 u6:0]  D[d3:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120212  U[u0:2 u1:0 u2:0 u4:1 u6:0]  D[d3:0 d5:1 d7:0 d8:1]`
+
+## G06 — word=UUUDUDUDD bites=(3,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01121`:
+
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012102121  U[u0:2 u1:0 u2:0 u4:1 u6:0]  D[p3_8:2 p5_7:0]`
+
+## G07 — word=UUUDUDDUD bites=-
+
+5 colouring(s) with up-tooth sequence `01121`:
+
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012102012  U[u0:2 u1:0 u2:0 u4:1 u7:0]  D[d3:2 d5:1 d6:2 d8:1]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012102021  U[u0:2 u1:0 u2:0 u4:1 u7:0]  D[d3:2 d5:1 d6:1 d8:2]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012102121  U[u0:2 u1:0 u2:0 u4:1 u7:0]  D[d3:2 d5:0 d6:0 d8:2]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120121  U[u0:2 u1:0 u2:0 u4:1 u7:0]  D[d3:0 d5:2 d6:0 d8:2]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120212  U[u0:2 u1:0 u2:0 u4:1 u7:0]  D[d3:0 d5:1 d6:0 d8:1]`
+
+## G09 — word=UUUDDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `01121`:
+
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120212  U[u0:2 u1:0 u2:0 u5:1 u6:0]  D[d3:0 d4:1 d7:0 d8:1]`
+
+## G11 — word=UUDUUDUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01121`:
+
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120121  U[u0:2 u1:0 u3:0 u4:1 u6:0]  D[d2:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120212  U[u0:2 u1:0 u3:0 u4:1 u6:0]  D[d2:0 d5:1 d7:0 d8:1]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `01121`:
+
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120212  U[u0:2 u1:0 u3:0 u5:1 u6:0]  D[d2:0 d4:1 d7:0 d8:1]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `01121`:
+
+- up apexes (raw labels) `20010` → canonical `01121`  ·  `A=012120212  U[u0:2 u1:0 u3:0 u5:1 u7:0]  D[d2:0 d4:1 d6:0 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01121.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01121.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01200.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01200.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01200.md
@@ -0,0 +1,125 @@
+# Up-tooth apex sequence `01200`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 3×colour0, 1×colour1, 1×colour2.
+- Realised by **15** of 18 M(T) (dihedral classes).
+- **39** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_01200.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUDDDD bites=-
+
+6 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u3:2 u4:2]  D[d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010102  U[u0:2 u1:0 u2:1 u3:2 u4:2]  D[d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010121  U[u0:2 u1:0 u2:1 u3:2 u4:2]  D[d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010201  U[u0:2 u1:0 u2:1 u3:2 u4:2]  D[d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010202  U[u0:2 u1:0 u2:1 u3:2 u4:2]  D[d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010212  U[u0:2 u1:0 u2:1 u3:2 u4:2]  D[d5:1 d6:0 d7:0 d8:1]`
+
+## G01 — word=UUUUDUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u3:2 u5:2]  D[d4:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010102  U[u0:2 u1:0 u2:1 u3:2 u5:2]  D[d4:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010121  U[u0:2 u1:0 u2:1 u3:2 u5:2]  D[d4:2 d6:0 d7:0 d8:2]`
+
+## G02 — word=UUUUDDUDD bites=-
+
+5 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u3:2 u6:2]  D[d4:2 d5:2 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010102  U[u0:2 u1:0 u2:1 u3:2 u6:2]  D[d4:2 d5:2 d7:1 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012012012  U[u0:2 u1:0 u2:1 u3:2 u6:2]  D[d4:0 d5:1 d7:0 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012012101  U[u0:2 u1:0 u2:1 u3:2 u6:2]  D[d4:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012012102  U[u0:2 u1:0 u2:1 u3:2 u6:2]  D[d4:0 d5:0 d7:1 d8:1]`
+
+## G03 — word=UUUUDDUDD bites=(4,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u3:2 u6:2]  D[p4_8:2 p5_7:2]`
+
+## G04 — word=UUUDUUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u4:2 u5:2]  D[d3:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010102  U[u0:2 u1:0 u2:1 u4:2 u5:2]  D[d3:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010121  U[u0:2 u1:0 u2:1 u4:2 u5:2]  D[d3:2 d6:0 d7:0 d8:2]`
+
+## G05 — word=UUUDUDUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u4:2 u6:2]  D[d3:2 d5:2 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010102  U[u0:2 u1:0 u2:1 u4:2 u6:2]  D[d3:2 d5:2 d7:1 d8:1]`
+
+## G06 — word=UUUDUDUDD bites=(3,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u4:2 u6:2]  D[p3_8:2 p5_7:2]`
+
+## G07 — word=UUUDUDDUD bites=-
+
+2 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u4:2 u7:2]  D[d3:2 d5:2 d6:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010201  U[u0:2 u1:0 u2:1 u4:2 u7:2]  D[d3:2 d5:1 d6:1 d8:2]`
+
+## G08 — word=UUUDUDDUD bites=(3,5),(6,8)
+
+1 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u4:2 u7:2]  D[p3_5:2 p6_8:2]`
+
+## G09 — word=UUUDDUUDD bites=-
+
+5 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u5:2 u6:2]  D[d3:2 d4:2 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010102  U[u0:2 u1:0 u2:1 u5:2 u6:2]  D[d3:2 d4:2 d7:1 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012020101  U[u0:2 u1:0 u2:1 u5:2 u6:2]  D[d3:1 d4:1 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012020102  U[u0:2 u1:0 u2:1 u5:2 u6:2]  D[d3:1 d4:1 d7:1 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012021012  U[u0:2 u1:0 u2:1 u5:2 u6:2]  D[d3:1 d4:0 d7:0 d8:1]`
+
+## G10 — word=UUUDDUUDD bites=(3,8),(4,7)
+
+3 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012010101  U[u0:2 u1:0 u2:1 u5:2 u6:2]  D[p3_8:2 p4_7:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012020102  U[u0:2 u1:0 u2:1 u5:2 u6:2]  D[p3_8:1 p4_7:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012021012  U[u0:2 u1:0 u2:1 u5:2 u6:2]  D[p3_8:1 p4_7:0]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+3 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012020101  U[u0:2 u1:0 u3:1 u5:2 u6:2]  D[d2:1 d4:1 d7:2 d8:2]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012020102  U[u0:2 u1:0 u3:1 u5:2 u6:2]  D[d2:1 d4:1 d7:1 d8:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012021012  U[u0:2 u1:0 u3:1 u5:2 u6:2]  D[d2:1 d4:0 d7:0 d8:1]`
+
+## G14 — word=UUDUDUUDD bites=(2,8),(4,7)
+
+2 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012020102  U[u0:2 u1:0 u3:1 u5:2 u6:2]  D[p2_8:1 p4_7:1]`
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012021012  U[u0:2 u1:0 u3:1 u5:2 u6:2]  D[p2_8:1 p4_7:0]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012020101  U[u0:2 u1:0 u3:1 u5:2 u7:2]  D[d2:1 d4:1 d6:2 d8:2]`
+
+## G16 — word=UUDUDUDUD bites=(2,4),(6,8)
+
+1 colouring(s) with up-tooth sequence `01200`:
+
+- up apexes (raw labels) `20122` → canonical `01200`  ·  `A=012020101  U[u0:2 u1:0 u3:1 u5:2 u7:2]  D[p2_4:1 p6_8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01200.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01200.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01200.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01200.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01211.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01211.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01211.md
@@ -0,0 +1,97 @@
+# Up-tooth apex sequence `01211`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 1×colour0, 3×colour1, 1×colour2.
+- Realised by **12** of 18 M(T) (dihedral classes).
+- **26** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_01211.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G04 — word=UUUDUUDDD bites=-
+
+6 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012101  U[u0:2 u1:0 u2:1 u4:0 u5:0]  D[d3:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012102  U[u0:2 u1:0 u2:1 u4:0 u5:0]  D[d3:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012121  U[u0:2 u1:0 u2:1 u4:0 u5:0]  D[d3:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021201  U[u0:2 u1:0 u2:1 u4:0 u5:0]  D[d3:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021202  U[u0:2 u1:0 u2:1 u4:0 u5:0]  D[d3:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u2:1 u4:0 u5:0]  D[d3:1 d6:0 d7:0 d8:1]`
+
+## G05 — word=UUUDUDUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012121  U[u0:2 u1:0 u2:1 u4:0 u6:0]  D[d3:2 d5:0 d7:0 d8:2]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u2:1 u4:0 u6:0]  D[d3:1 d5:0 d7:0 d8:1]`
+
+## G06 — word=UUUDUDUDD bites=(3,8),(5,7)
+
+2 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012121  U[u0:2 u1:0 u2:1 u4:0 u6:0]  D[p3_8:2 p5_7:0]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u2:1 u4:0 u6:0]  D[p3_8:1 p5_7:0]`
+
+## G07 — word=UUUDUDDUD bites=-
+
+6 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012012  U[u0:2 u1:0 u2:1 u4:0 u7:0]  D[d3:2 d5:1 d6:2 d8:1]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012021  U[u0:2 u1:0 u2:1 u4:0 u7:0]  D[d3:2 d5:1 d6:1 d8:2]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012121  U[u0:2 u1:0 u2:1 u4:0 u7:0]  D[d3:2 d5:0 d6:0 d8:2]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021012  U[u0:2 u1:0 u2:1 u4:0 u7:0]  D[d3:1 d5:2 d6:2 d8:1]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021021  U[u0:2 u1:0 u2:1 u4:0 u7:0]  D[d3:1 d5:2 d6:1 d8:2]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u2:1 u4:0 u7:0]  D[d3:1 d5:0 d6:0 d8:1]`
+
+## G09 — word=UUUDDUUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012121  U[u0:2 u1:0 u2:1 u5:0 u6:0]  D[d3:2 d4:0 d7:0 d8:2]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u2:1 u5:0 u6:0]  D[d3:1 d4:0 d7:0 d8:1]`
+
+## G10 — word=UUUDDUUDD bites=(3,8),(4,7)
+
+2 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012012121  U[u0:2 u1:0 u2:1 u5:0 u6:0]  D[p3_8:2 p4_7:0]`
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u2:1 u5:0 u6:0]  D[p3_8:1 p4_7:0]`
+
+## G11 — word=UUDUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u3:1 u4:0 u6:0]  D[d2:1 d5:0 d7:0 d8:1]`
+
+## G12 — word=UUDUUDUDD bites=(2,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u3:1 u4:0 u6:0]  D[p2_8:1 p5_7:0]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u3:1 u5:0 u6:0]  D[d2:1 d4:0 d7:0 d8:1]`
+
+## G14 — word=UUDUDUUDD bites=(2,8),(4,7)
+
+1 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u3:1 u5:0 u6:0]  D[p2_8:1 p4_7:0]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u3:1 u5:0 u7:0]  D[d2:1 d4:0 d6:0 d8:1]`
+
+## G17 — word=UUDUDUDUD bites=(2,8),(4,6)
+
+1 colouring(s) with up-tooth sequence `01211`:
+
+- up apexes (raw labels) `20100` → canonical `01211`  ·  `A=012021212  U[u0:2 u1:0 u3:1 u5:0 u7:0]  D[p2_8:1 p4_6:0]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01211.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01211.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01211.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01211.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01222.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01222.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01222.md
@@ -0,0 +1,142 @@
+# Up-tooth apex sequence `01222`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 5 up teeth**.
+
+- Colour multiset: 1×colour0, 1×colour1, 3×colour2.
+- Realised by **18** of 18 M(T) (dihedral classes).
+- **41** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_01222.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUDDDD bites=-
+
+6 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020101  U[u0:2 u1:0 u2:1 u3:1 u4:1]  D[d5:2 d6:2 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020102  U[u0:2 u1:0 u2:1 u3:1 u4:1]  D[d5:2 d6:2 d7:1 d8:1]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020121  U[u0:2 u1:0 u2:1 u3:1 u4:1]  D[d5:2 d6:0 d7:0 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020201  U[u0:2 u1:0 u2:1 u3:1 u4:1]  D[d5:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u3:1 u4:1]  D[d5:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020212  U[u0:2 u1:0 u2:1 u3:1 u4:1]  D[d5:1 d6:0 d7:0 d8:1]`
+
+## G01 — word=UUUUDUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020201  U[u0:2 u1:0 u2:1 u3:1 u5:1]  D[d4:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u3:1 u5:1]  D[d4:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020212  U[u0:2 u1:0 u2:1 u3:1 u5:1]  D[d4:1 d6:0 d7:0 d8:1]`
+
+## G02 — word=UUUUDDUDD bites=-
+
+5 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020201  U[u0:2 u1:0 u2:1 u3:1 u6:1]  D[d4:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u3:1 u6:1]  D[d4:1 d5:1 d7:1 d8:1]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012021021  U[u0:2 u1:0 u2:1 u3:1 u6:1]  D[d4:0 d5:2 d7:0 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012021201  U[u0:2 u1:0 u2:1 u3:1 u6:1]  D[d4:0 d5:0 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012021202  U[u0:2 u1:0 u2:1 u3:1 u6:1]  D[d4:0 d5:0 d7:1 d8:1]`
+
+## G03 — word=UUUUDDUDD bites=(4,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u3:1 u6:1]  D[p4_8:1 p5_7:1]`
+
+## G04 — word=UUUDUUDDD bites=-
+
+3 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020201  U[u0:2 u1:0 u2:1 u4:1 u5:1]  D[d3:1 d6:1 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u4:1 u5:1]  D[d3:1 d6:1 d7:1 d8:1]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020212  U[u0:2 u1:0 u2:1 u4:1 u5:1]  D[d3:1 d6:0 d7:0 d8:1]`
+
+## G05 — word=UUUDUDUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020201  U[u0:2 u1:0 u2:1 u4:1 u6:1]  D[d3:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u4:1 u6:1]  D[d3:1 d5:1 d7:1 d8:1]`
+
+## G06 — word=UUUDUDUDD bites=(3,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u4:1 u6:1]  D[p3_8:1 p5_7:1]`
+
+## G07 — word=UUUDUDDUD bites=-
+
+2 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020102  U[u0:2 u1:0 u2:1 u4:1 u7:1]  D[d3:1 d5:2 d6:2 d8:1]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u4:1 u7:1]  D[d3:1 d5:1 d6:1 d8:1]`
+
+## G08 — word=UUUDUDDUD bites=(3,5),(6,8)
+
+1 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u4:1 u7:1]  D[p3_5:1 p6_8:1]`
+
+## G09 — word=UUUDDUUDD bites=-
+
+5 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012010201  U[u0:2 u1:0 u2:1 u5:1 u6:1]  D[d3:2 d4:2 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012010202  U[u0:2 u1:0 u2:1 u5:1 u6:1]  D[d3:2 d4:2 d7:1 d8:1]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012012021  U[u0:2 u1:0 u2:1 u5:1 u6:1]  D[d3:2 d4:0 d7:0 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020201  U[u0:2 u1:0 u2:1 u5:1 u6:1]  D[d3:1 d4:1 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u5:1 u6:1]  D[d3:1 d4:1 d7:1 d8:1]`
+
+## G10 — word=UUUDDUUDD bites=(3,8),(4,7)
+
+3 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012010201  U[u0:2 u1:0 u2:1 u5:1 u6:1]  D[p3_8:2 p4_7:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012012021  U[u0:2 u1:0 u2:1 u5:1 u6:1]  D[p3_8:2 p4_7:0]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u2:1 u5:1 u6:1]  D[p3_8:1 p4_7:1]`
+
+## G11 — word=UUDUUDUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020201  U[u0:2 u1:0 u3:1 u4:1 u6:1]  D[d2:1 d5:1 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u3:1 u4:1 u6:1]  D[d2:1 d5:1 d7:1 d8:1]`
+
+## G12 — word=UUDUUDUDD bites=(2,8),(5,7)
+
+1 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u3:1 u4:1 u6:1]  D[p2_8:1 p5_7:1]`
+
+## G13 — word=UUDUDUUDD bites=-
+
+2 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020201  U[u0:2 u1:0 u3:1 u5:1 u6:1]  D[d2:1 d4:1 d7:2 d8:2]`
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u3:1 u5:1 u6:1]  D[d2:1 d4:1 d7:1 d8:1]`
+
+## G14 — word=UUDUDUUDD bites=(2,8),(4,7)
+
+1 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u3:1 u5:1 u6:1]  D[p2_8:1 p4_7:1]`
+
+## G15 — word=UUDUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u3:1 u5:1 u7:1]  D[d2:1 d4:1 d6:1 d8:1]`
+
+## G16 — word=UUDUDUDUD bites=(2,4),(6,8)
+
+1 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u3:1 u5:1 u7:1]  D[p2_4:1 p6_8:1]`
+
+## G17 — word=UUDUDUDUD bites=(2,8),(4,6)
+
+1 colouring(s) with up-tooth sequence `01222`:
+
+- up apexes (raw labels) `20111` → canonical `01222`  ·  `A=012020202  U[u0:2 u1:0 u3:1 u5:1 u7:1]  D[p2_8:1 p4_6:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01222.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/seq_01222.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/summary.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m5/summary.md
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+# Up-tooth apex sequences of Kempe-balanced colourings (n=9, m=5)
+
+Every full medial tire graph M(T) with |A(T)| = 9 and exactly 5 up teeth, one representative per dihedral class: **18 M(T)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the up-tooth apex colour sequence u0<u1<... in cyclic order, and reduce it modulo colour permutation (NOT dihedral symmetry).
+
+- Total Kempe-balanced colourings (mod colour permutation): **285**.
+- Distinct canonical up-tooth sequences overall: **10**.
+
+## Distinct canonical up-tooth sequences
+
+| sequence | colour multiset | #M(T) realising | #colourings |
+|---|---|---|---|
+| `00012` | 3+1+1 | 18 | 49 |
+| `00102` | 3+1+1 | 11 | 26 |
+| `00120` | 3+1+1 | 16 | 39 |
+| `01002` | 3+1+1 | 5 | 9 |
+| `01020` | 3+1+1 | 4 | 7 |
+| `01112` | 3+1+1 | 13 | 32 |
+| `01121` | 3+1+1 | 8 | 17 |
+| `01200` | 3+1+1 | 15 | 39 |
+| `01211` | 3+1+1 | 12 | 26 |
+| `01222` | 3+1+1 | 18 | 41 |
+
+Note: every realised sequence has its three colour-counts of **equal parity** — exactly the outer-face Kempe-parity constraint (each colour pair meets the up-tooth apexes an even number of times). With m = 5 up teeth (m is odd) every count must be **odd**, so the only admissible colour multisets are 3+1+1.
+
+## Step 4 — grouping M(T) by their set of unique up-tooth sequences
+
+The 18 M(T) fall into **8** groups by the set of canonical up-tooth sequences they realise:
+
+| #M(T) | set of up-tooth sequences | M(T) ids |
+|---|---|---|
+| 6 | { `00012`, `00120`, `01112`, `01200`, `01222` } | G00, G01, G02, G03, G08, G16 |
+| 3 | { `00012`, `00102`, `00120`, `01112`, `01121`, `01200`, `01211`, `01222` } | G05, G07, G09 |
+| 2 | { `00012`, `00102`, `01121`, `01200`, `01211`, `01222` } | G04, G06 |
+| 2 | { `00012`, `00102`, `00120`, `01002`, `01211`, `01222` } | G12, G17 |
+| 2 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } | G13, G15 |
+| 1 | { `00012`, `00120`, `01112`, `01200`, `01211`, `01222` } | G10 |
+| 1 | { `00012`, `00102`, `00120`, `01020`, `01200`, `01211`, `01222` } | G14 |
+| 1 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01211`, `01222` } | G11 |
+
+## M(T) atlas (ids)
+
+| id | word / bites | #Kempe-balanced | up-tooth sequence set |
+|---|---|---|---|
+| G00 | word=UUUUUDDDD bites=- | 30 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
+| G01 | word=UUUUDUDDD bites=- | 15 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
+| G02 | word=UUUUDDUDD bites=- | 25 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
+| G03 | word=UUUUDDUDD bites=(4,8),(5,7) | 5 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
+| G04 | word=UUUDUUDDD bites=- | 21 | { `00012`, `00102`, `01121`, `01200`, `01211`, `01222` } |
+| G05 | word=UUUDUDUDD bites=- | 24 | { `00012`, `00102`, `00120`, `01112`, `01121`, `01200`, `01211`, `01222` } |
+| G06 | word=UUUDUDUDD bites=(3,8),(5,7) | 7 | { `00012`, `00102`, `01121`, `01200`, `01211`, `01222` } |
+| G07 | word=UUUDUDDUD bites=- | 28 | { `00012`, `00102`, `00120`, `01112`, `01121`, `01200`, `01211`, `01222` } |
+| G08 | word=UUUDUDDUD bites=(3,5),(6,8) | 5 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
+| G09 | word=UUUDDUUDD bites=- | 27 | { `00012`, `00102`, `00120`, `01112`, `01121`, `01200`, `01211`, `01222` } |
+| G10 | word=UUUDDUUDD bites=(3,8),(4,7) | 11 | { `00012`, `00120`, `01112`, `01200`, `01211`, `01222` } |
+| G11 | word=UUDUUDUDD bites=- | 22 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01211`, `01222` } |
+| G12 | word=UUDUUDUDD bites=(2,8),(5,7) | 7 | { `00012`, `00102`, `00120`, `01002`, `01211`, `01222` } |
+| G13 | word=UUDUDUUDD bites=- | 18 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
+| G14 | word=UUDUDUUDD bites=(2,8),(4,7) | 9 | { `00012`, `00102`, `00120`, `01020`, `01200`, `01211`, `01222` } |
+| G15 | word=UUDUDUDUD bites=- | 19 | { `00012`, `00102`, `00120`, `01002`, `01020`, `01112`, `01121`, `01200`, `01211`, `01222` } |
+| G16 | word=UUDUDUDUD bites=(2,4),(6,8) | 5 | { `00012`, `00120`, `01112`, `01200`, `01222` } |
+| G17 | word=UUDUDUDUD bites=(2,8),(4,6) | 7 | { `00012`, `00102`, `00120`, `01002`, `01211`, `01222` } |
+
+## Per-sequence notes
+
+- [`00012`](seq_00012.md) — figure `seq_00012.png`
+- [`00102`](seq_00102.md) — figure `seq_00102.png`
+- [`00120`](seq_00120.md) — figure `seq_00120.png`
+- [`01002`](seq_01002.md) — figure `seq_01002.png`
+- [`01020`](seq_01020.md) — figure `seq_01020.png`
+- [`01112`](seq_01112.md) — figure `seq_01112.png`
+- [`01121`](seq_01121.md) — figure `seq_01121.png`
+- [`01200`](seq_01200.md) — figure `seq_01200.png`
+- [`01211`](seq_01211.md) — figure `seq_01211.png`
+- [`01222`](seq_01222.md) — figure `seq_01222.png`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000000.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000000.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000000.md
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+# Up-tooth apex sequence `000000`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 6×colour0.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **5** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_000000.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `000000`:
+
+- up apexes (raw labels) `222222` → canonical `000000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u3:2 u4:2 u5:2]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `222222` → canonical `000000`  ·  `A=010101021  U[u0:2 u1:2 u2:2 u3:2 u4:2 u5:2]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `000000`:
+
+- up apexes (raw labels) `222222` → canonical `000000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u3:2 u4:2 u6:2]  D[d5:2 d7:0 d8:1]`
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `000000`:
+
+- up apexes (raw labels) `222222` → canonical `000000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u3:2 u5:2 u6:2]  D[d4:2 d7:0 d8:1]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `000000`:
+
+- up apexes (raw labels) `222222` → canonical `000000`  ·  `A=010101012  U[u0:2 u1:2 u2:2 u4:2 u5:2 u6:2]  D[d3:2 d7:0 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000000.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000000.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000011.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000011.md
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+# Up-tooth apex sequence `000011`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **7** of 7 M(T) (dihedral classes).
+- **12** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_000011.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `000011`:
+
+- up apexes (raw labels) `222211` → canonical `000011`  ·  `A=010102012  U[u0:2 u1:2 u2:2 u3:2 u4:1 u5:1]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `222211` → canonical `000011`  ·  `A=010102021  U[u0:2 u1:2 u2:2 u3:2 u4:1 u5:1]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `000011`:
+
+- up apexes (raw labels) `222211` → canonical `000011`  ·  `A=010102021  U[u0:2 u1:2 u2:2 u3:2 u4:1 u6:1]  D[d5:1 d7:0 d8:2]`
+
+## G02 — word=UUUUDUUDD bites=-
+
+3 colouring(s) with up-tooth sequence `000011`:
+
+- up apexes (raw labels) `222200` → canonical `000011`  ·  `A=010101212  U[u0:2 u1:2 u2:2 u3:2 u5:0 u6:0]  D[d4:2 d7:0 d8:1]`
+- up apexes (raw labels) `222211` → canonical `000011`  ·  `A=010102021  U[u0:2 u1:2 u2:2 u3:2 u5:1 u6:1]  D[d4:1 d7:0 d8:2]`
+- up apexes (raw labels) `222200` → canonical `000011`  ·  `A=010102121  U[u0:2 u1:2 u2:2 u3:2 u5:0 u6:0]  D[d4:1 d7:0 d8:2]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+2 colouring(s) with up-tooth sequence `000011`:
+
+- up apexes (raw labels) `222200` → canonical `000011`  ·  `A=010101212  U[u0:2 u1:2 u2:2 u3:2 u5:0 u7:0]  D[d4:2 d6:0 d8:1]`
+- up apexes (raw labels) `222200` → canonical `000011`  ·  `A=010102121  U[u0:2 u1:2 u2:2 u3:2 u5:0 u7:0]  D[d4:1 d6:0 d8:2]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `000011`:
+
+- up apexes (raw labels) `222200` → canonical `000011`  ·  `A=010101212  U[u0:2 u1:2 u2:2 u4:2 u5:0 u6:0]  D[d3:2 d7:0 d8:1]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `000011`:
+
+- up apexes (raw labels) `222200` → canonical `000011`  ·  `A=010101212  U[u0:2 u1:2 u2:2 u4:2 u5:0 u7:0]  D[d3:2 d6:0 d8:1]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+2 colouring(s) with up-tooth sequence `000011`:
+
+- up apexes (raw labels) `222211` → canonical `000011`  ·  `A=010101202  U[u0:2 u1:2 u3:2 u4:2 u6:1 u7:1]  D[d2:2 d5:0 d8:1]`
+- up apexes (raw labels) `222200` → canonical `000011`  ·  `A=010101212  U[u0:2 u1:2 u3:2 u4:2 u6:0 u7:0]  D[d2:2 d5:0 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000011.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000011.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000011.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000011.png
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index 0000000..abf6431
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000101.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000101.md
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index 0000000..72bd1ce
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000101.md
@@ -0,0 +1,39 @@
+# Up-tooth apex sequence `000101`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **8** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_000101.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `000101`:
+
+- up apexes (raw labels) `222020` → canonical `000101`  ·  `A=010120121  U[u0:2 u1:2 u2:2 u3:0 u5:2 u6:0]  D[d4:1 d7:0 d8:2]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+3 colouring(s) with up-tooth sequence `000101`:
+
+- up apexes (raw labels) `222020` → canonical `000101`  ·  `A=010120121  U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0]  D[d4:1 d6:0 d8:2]`
+- up apexes (raw labels) `222020` → canonical `000101`  ·  `A=010121012  U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0]  D[d4:0 d6:2 d8:1]`
+- up apexes (raw labels) `222020` → canonical `000101`  ·  `A=010121021  U[u0:2 u1:2 u2:2 u3:0 u5:2 u7:0]  D[d4:0 d6:1 d8:2]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+3 colouring(s) with up-tooth sequence `000101`:
+
+- up apexes (raw labels) `222121` → canonical `000101`  ·  `A=010120102  U[u0:2 u1:2 u2:2 u4:1 u5:2 u7:1]  D[d3:0 d6:2 d8:1]`
+- up apexes (raw labels) `222020` → canonical `000101`  ·  `A=010121012  U[u0:2 u1:2 u2:2 u4:0 u5:2 u7:0]  D[d3:0 d6:2 d8:1]`
+- up apexes (raw labels) `222020` → canonical `000101`  ·  `A=010121021  U[u0:2 u1:2 u2:2 u4:0 u5:2 u7:0]  D[d3:0 d6:1 d8:2]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `000101`:
+
+- up apexes (raw labels) `222121` → canonical `000101`  ·  `A=010102102  U[u0:2 u1:2 u3:2 u4:1 u6:2 u7:1]  D[d2:2 d5:0 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000101.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000101.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000101.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000101.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000110.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000110.md
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index 0000000..ae4c6d4
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000110.md
@@ -0,0 +1,43 @@
+# Up-tooth apex sequence `000110`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **5** of 7 M(T) (dihedral classes).
+- **7** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_000110.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `000110`:
+
+- up apexes (raw labels) `222002` → canonical `000110`  ·  `A=010121012  U[u0:2 u1:2 u2:2 u3:0 u4:0 u5:2]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `222002` → canonical `000110`  ·  `A=010121021  U[u0:2 u1:2 u2:2 u3:0 u4:0 u5:2]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `000110`:
+
+- up apexes (raw labels) `222002` → canonical `000110`  ·  `A=010121012  U[u0:2 u1:2 u2:2 u3:0 u4:0 u6:2]  D[d5:2 d7:0 d8:1]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `000110`:
+
+- up apexes (raw labels) `222002` → canonical `000110`  ·  `A=010121201  U[u0:2 u1:2 u2:2 u3:0 u5:0 u7:2]  D[d4:0 d6:1 d8:2]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `000110`:
+
+- up apexes (raw labels) `222112` → canonical `000110`  ·  `A=010102012  U[u0:2 u1:2 u2:2 u4:1 u5:1 u6:2]  D[d3:2 d7:0 d8:1]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+2 colouring(s) with up-tooth sequence `000110`:
+
+- up apexes (raw labels) `222112` → canonical `000110`  ·  `A=010120201  U[u0:2 u1:2 u2:2 u4:1 u5:1 u7:2]  D[d3:0 d6:1 d8:2]`
+- up apexes (raw labels) `222002` → canonical `000110`  ·  `A=010121201  U[u0:2 u1:2 u2:2 u4:0 u5:0 u7:2]  D[d3:0 d6:1 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000110.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000110.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000110.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_000110.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001001.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001001.md
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index 0000000..110c6ef
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001001.md
@@ -0,0 +1,23 @@
+# Up-tooth apex sequence `001001`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **2** of 7 M(T) (dihedral classes).
+- **2** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_001001.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001001`:
+
+- up apexes (raw labels) `221221` → canonical `001001`  ·  `A=010201021  U[u0:2 u1:2 u2:1 u4:2 u5:2 u6:1]  D[d3:1 d7:0 d8:2]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `001001`:
+
+- up apexes (raw labels) `221221` → canonical `001001`  ·  `A=010210102  U[u0:2 u1:2 u2:1 u4:2 u5:2 u7:1]  D[d3:0 d6:2 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001001.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001001.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001001.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001001.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001010.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001010.md
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--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001010.md
@@ -0,0 +1,23 @@
+# Up-tooth apex sequence `001010`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **2** of 7 M(T) (dihedral classes).
+- **2** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_001010.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `001010`:
+
+- up apexes (raw labels) `221212` → canonical `001010`  ·  `A=010210201  U[u0:2 u1:2 u2:1 u4:2 u5:1 u7:2]  D[d3:0 d6:1 d8:2]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `001010`:
+
+- up apexes (raw labels) `221212` → canonical `001010`  ·  `A=010201201  U[u0:2 u1:2 u3:1 u4:2 u6:1 u7:2]  D[d2:1 d5:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001010.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001010.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001010.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001010.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001100.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001100.md
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--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001100.md
@@ -0,0 +1,37 @@
+# Up-tooth apex sequence `001100`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **6** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_001100.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `001100`:
+
+- up apexes (raw labels) `221122` → canonical `001100`  ·  `A=010201012  U[u0:2 u1:2 u2:1 u3:1 u4:2 u5:2]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `221122` → canonical `001100`  ·  `A=010201021  U[u0:2 u1:2 u2:1 u3:1 u4:2 u5:2]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001100`:
+
+- up apexes (raw labels) `221122` → canonical `001100`  ·  `A=010201012  U[u0:2 u1:2 u2:1 u3:1 u4:2 u6:2]  D[d5:2 d7:0 d8:1]`
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001100`:
+
+- up apexes (raw labels) `221122` → canonical `001100`  ·  `A=010201012  U[u0:2 u1:2 u2:1 u3:1 u5:2 u6:2]  D[d4:2 d7:0 d8:1]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+2 colouring(s) with up-tooth sequence `001100`:
+
+- up apexes (raw labels) `221122` → canonical `001100`  ·  `A=010202101  U[u0:2 u1:2 u3:1 u4:1 u6:2 u7:2]  D[d2:1 d5:0 d8:2]`
+- up apexes (raw labels) `220022` → canonical `001100`  ·  `A=010212101  U[u0:2 u1:2 u3:0 u4:0 u6:2 u7:2]  D[d2:1 d5:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001100.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001100.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001100.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001100.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001111.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001111.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001111.md
@@ -0,0 +1,43 @@
+# Up-tooth apex sequence `001111`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 4×colour1.
+- Realised by **5** of 7 M(T) (dihedral classes).
+- **7** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_001111.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `001111`:
+
+- up apexes (raw labels) `221111` → canonical `001111`  ·  `A=010202012  U[u0:2 u1:2 u2:1 u3:1 u4:1 u5:1]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `221111` → canonical `001111`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u3:1 u4:1 u5:1]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001111`:
+
+- up apexes (raw labels) `221111` → canonical `001111`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u3:1 u4:1 u6:1]  D[d5:1 d7:0 d8:2]`
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001111`:
+
+- up apexes (raw labels) `221111` → canonical `001111`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u3:1 u5:1 u6:1]  D[d4:1 d7:0 d8:2]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001111`:
+
+- up apexes (raw labels) `221111` → canonical `001111`  ·  `A=010202021  U[u0:2 u1:2 u2:1 u4:1 u5:1 u6:1]  D[d3:1 d7:0 d8:2]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+2 colouring(s) with up-tooth sequence `001111`:
+
+- up apexes (raw labels) `220000` → canonical `001111`  ·  `A=010121212  U[u0:2 u1:2 u3:0 u4:0 u6:0 u7:0]  D[d2:2 d5:0 d8:1]`
+- up apexes (raw labels) `220000` → canonical `001111`  ·  `A=010212121  U[u0:2 u1:2 u3:0 u4:0 u6:0 u7:0]  D[d2:1 d5:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001111.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001111.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001111.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001111.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001122.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001122.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001122.md
@@ -0,0 +1,44 @@
+# Up-tooth apex sequence `001122`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **5** of 7 M(T) (dihedral classes).
+- **8** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_001122.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G02 — word=UUUUDUUDD bites=-
+
+2 colouring(s) with up-tooth sequence `001122`:
+
+- up apexes (raw labels) `221100` → canonical `001122`  ·  `A=010201212  U[u0:2 u1:2 u2:1 u3:1 u5:0 u6:0]  D[d4:2 d7:0 d8:1]`
+- up apexes (raw labels) `221100` → canonical `001122`  ·  `A=010202121  U[u0:2 u1:2 u2:1 u3:1 u5:0 u6:0]  D[d4:1 d7:0 d8:2]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+2 colouring(s) with up-tooth sequence `001122`:
+
+- up apexes (raw labels) `221100` → canonical `001122`  ·  `A=010201212  U[u0:2 u1:2 u2:1 u3:1 u5:0 u7:0]  D[d4:2 d6:0 d8:1]`
+- up apexes (raw labels) `221100` → canonical `001122`  ·  `A=010202121  U[u0:2 u1:2 u2:1 u3:1 u5:0 u7:0]  D[d4:1 d6:0 d8:2]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001122`:
+
+- up apexes (raw labels) `221100` → canonical `001122`  ·  `A=010202121  U[u0:2 u1:2 u2:1 u4:1 u5:0 u6:0]  D[d3:1 d7:0 d8:2]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `001122`:
+
+- up apexes (raw labels) `221100` → canonical `001122`  ·  `A=010202121  U[u0:2 u1:2 u2:1 u4:1 u5:0 u7:0]  D[d3:1 d6:0 d8:2]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+2 colouring(s) with up-tooth sequence `001122`:
+
+- up apexes (raw labels) `220011` → canonical `001122`  ·  `A=010121202  U[u0:2 u1:2 u3:0 u4:0 u6:1 u7:1]  D[d2:2 d5:0 d8:1]`
+- up apexes (raw labels) `221100` → canonical `001122`  ·  `A=010202121  U[u0:2 u1:2 u3:1 u4:1 u6:0 u7:0]  D[d2:1 d5:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001122.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001122.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001122.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001122.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001212.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001212.md
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@@ -0,0 +1,32 @@
+# Up-tooth apex sequence `001212`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **3** of 7 M(T) (dihedral classes).
+- **6** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_001212.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001212`:
+
+- up apexes (raw labels) `221010` → canonical `001212`  ·  `A=010210212  U[u0:2 u1:2 u2:1 u3:0 u5:1 u6:0]  D[d4:2 d7:0 d8:1]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+3 colouring(s) with up-tooth sequence `001212`:
+
+- up apexes (raw labels) `221010` → canonical `001212`  ·  `A=010210212  U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0]  D[d4:2 d6:0 d8:1]`
+- up apexes (raw labels) `221010` → canonical `001212`  ·  `A=010212012  U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0]  D[d4:0 d6:2 d8:1]`
+- up apexes (raw labels) `221010` → canonical `001212`  ·  `A=010212021  U[u0:2 u1:2 u2:1 u3:0 u5:1 u7:0]  D[d4:0 d6:1 d8:2]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+2 colouring(s) with up-tooth sequence `001212`:
+
+- up apexes (raw labels) `221010` → canonical `001212`  ·  `A=010212012  U[u0:2 u1:2 u2:1 u4:0 u5:1 u7:0]  D[d3:0 d6:2 d8:1]`
+- up apexes (raw labels) `221010` → canonical `001212`  ·  `A=010212021  U[u0:2 u1:2 u2:1 u4:0 u5:1 u7:0]  D[d3:0 d6:1 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001212.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001212.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001221.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001221.md
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@@ -0,0 +1,36 @@
+# Up-tooth apex sequence `001221`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **5** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_001221.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `001221`:
+
+- up apexes (raw labels) `221001` → canonical `001221`  ·  `A=010212012  U[u0:2 u1:2 u2:1 u3:0 u4:0 u5:1]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `221001` → canonical `001221`  ·  `A=010212021  U[u0:2 u1:2 u2:1 u3:0 u4:0 u5:1]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `001221`:
+
+- up apexes (raw labels) `221001` → canonical `001221`  ·  `A=010212021  U[u0:2 u1:2 u2:1 u3:0 u4:0 u6:1]  D[d5:1 d7:0 d8:2]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `001221`:
+
+- up apexes (raw labels) `221001` → canonical `001221`  ·  `A=010212102  U[u0:2 u1:2 u2:1 u3:0 u5:0 u7:1]  D[d4:0 d6:2 d8:1]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `001221`:
+
+- up apexes (raw labels) `221001` → canonical `001221`  ·  `A=010212102  U[u0:2 u1:2 u2:1 u4:0 u5:0 u7:1]  D[d3:0 d6:2 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001221.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_001221.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010001.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010001.md
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@@ -0,0 +1,17 @@
+# Up-tooth apex sequence `010001`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **1** of 7 M(T) (dihedral classes).
+- **1** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_010001.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `010001`:
+
+- up apexes (raw labels) `202220` → canonical `010001`  ·  `A=012101012  U[u0:2 u1:0 u3:2 u4:2 u6:2 u7:0]  D[d2:0 d5:2 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010001.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010001.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010100.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010100.md
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--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010100.md
@@ -0,0 +1,17 @@
+# Up-tooth apex sequence `010100`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **1** of 7 M(T) (dihedral classes).
+- **1** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_010100.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `010100`:
+
+- up apexes (raw labels) `202022` → canonical `010100`  ·  `A=012012101  U[u0:2 u1:0 u3:2 u4:0 u6:2 u7:2]  D[d2:1 d5:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010100.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010100.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010111.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010111.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010111.md
@@ -0,0 +1,17 @@
+# Up-tooth apex sequence `010111`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 4×colour1.
+- Realised by **1** of 7 M(T) (dihedral classes).
+- **1** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_010111.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `010111`:
+
+- up apexes (raw labels) `202000` → canonical `010111`  ·  `A=012012121  U[u0:2 u1:0 u3:2 u4:0 u6:0 u7:0]  D[d2:1 d5:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010111.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010111.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010111.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010111.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010221.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010221.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010221.md
@@ -0,0 +1,17 @@
+# Up-tooth apex sequence `010221`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **1** of 7 M(T) (dihedral classes).
+- **1** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_010221.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `010221`:
+
+- up apexes (raw labels) `202110` → canonical `010221`  ·  `A=012102021  U[u0:2 u1:0 u3:2 u4:1 u6:1 u7:0]  D[d2:0 d5:1 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010221.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010221.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010221.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_010221.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011000.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011000.md
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+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011000.md
@@ -0,0 +1,36 @@
+# Up-tooth apex sequence `011000`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 4×colour0, 2×colour1.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **5** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_011000.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `011000`:
+
+- up apexes (raw labels) `200222` → canonical `011000`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u3:2 u4:2 u5:2]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `200222` → canonical `011000`  ·  `A=012101021  U[u0:2 u1:0 u2:0 u3:2 u4:2 u5:2]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011000`:
+
+- up apexes (raw labels) `200222` → canonical `011000`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u3:2 u4:2 u6:2]  D[d5:2 d7:0 d8:1]`
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011000`:
+
+- up apexes (raw labels) `200222` → canonical `011000`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u3:2 u5:2 u6:2]  D[d4:2 d7:0 d8:1]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011000`:
+
+- up apexes (raw labels) `200222` → canonical `011000`  ·  `A=012101012  U[u0:2 u1:0 u2:0 u4:2 u5:2 u6:2]  D[d3:2 d7:0 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011000.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011000.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011000.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011000.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011011.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011011.md
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--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011011.md
@@ -0,0 +1,37 @@
+# Up-tooth apex sequence `011011`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 4×colour1.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **6** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_011011.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G02 — word=UUUUDUUDD bites=-
+
+2 colouring(s) with up-tooth sequence `011011`:
+
+- up apexes (raw labels) `200200` → canonical `011011`  ·  `A=012101212  U[u0:2 u1:0 u2:0 u3:2 u5:0 u6:0]  D[d4:2 d7:0 d8:1]`
+- up apexes (raw labels) `200200` → canonical `011011`  ·  `A=012102121  U[u0:2 u1:0 u2:0 u3:2 u5:0 u6:0]  D[d4:1 d7:0 d8:2]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+2 colouring(s) with up-tooth sequence `011011`:
+
+- up apexes (raw labels) `200200` → canonical `011011`  ·  `A=012101212  U[u0:2 u1:0 u2:0 u3:2 u5:0 u7:0]  D[d4:2 d6:0 d8:1]`
+- up apexes (raw labels) `200200` → canonical `011011`  ·  `A=012102121  U[u0:2 u1:0 u2:0 u3:2 u5:0 u7:0]  D[d4:1 d6:0 d8:2]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011011`:
+
+- up apexes (raw labels) `200200` → canonical `011011`  ·  `A=012101212  U[u0:2 u1:0 u2:0 u4:2 u5:0 u6:0]  D[d3:2 d7:0 d8:1]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `011011`:
+
+- up apexes (raw labels) `200200` → canonical `011011`  ·  `A=012101212  U[u0:2 u1:0 u2:0 u4:2 u5:0 u7:0]  D[d3:2 d6:0 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011011.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011011.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011011.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011011.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011022.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011022.md
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--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011022.md
@@ -0,0 +1,30 @@
+# Up-tooth apex sequence `011022`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **3** of 7 M(T) (dihedral classes).
+- **4** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_011022.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `011022`:
+
+- up apexes (raw labels) `200211` → canonical `011022`  ·  `A=012102012  U[u0:2 u1:0 u2:0 u3:2 u4:1 u5:1]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `200211` → canonical `011022`  ·  `A=012102021  U[u0:2 u1:0 u2:0 u3:2 u4:1 u5:1]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011022`:
+
+- up apexes (raw labels) `200211` → canonical `011022`  ·  `A=012102021  U[u0:2 u1:0 u2:0 u3:2 u4:1 u6:1]  D[d5:1 d7:0 d8:2]`
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011022`:
+
+- up apexes (raw labels) `200211` → canonical `011022`  ·  `A=012102021  U[u0:2 u1:0 u2:0 u3:2 u5:1 u6:1]  D[d4:1 d7:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011022.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011022.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011022.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011022.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011101.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011101.md
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index 0000000..c9bed81
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011101.md
@@ -0,0 +1,38 @@
+# Up-tooth apex sequence `011101`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 4×colour1.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **7** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_011101.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011101`:
+
+- up apexes (raw labels) `200020` → canonical `011101`  ·  `A=012120121  U[u0:2 u1:0 u2:0 u3:0 u5:2 u6:0]  D[d4:1 d7:0 d8:2]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+3 colouring(s) with up-tooth sequence `011101`:
+
+- up apexes (raw labels) `200020` → canonical `011101`  ·  `A=012120121  U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0]  D[d4:1 d6:0 d8:2]`
+- up apexes (raw labels) `200020` → canonical `011101`  ·  `A=012121012  U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0]  D[d4:0 d6:2 d8:1]`
+- up apexes (raw labels) `200020` → canonical `011101`  ·  `A=012121021  U[u0:2 u1:0 u2:0 u3:0 u5:2 u7:0]  D[d4:0 d6:1 d8:2]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+2 colouring(s) with up-tooth sequence `011101`:
+
+- up apexes (raw labels) `200020` → canonical `011101`  ·  `A=012121012  U[u0:2 u1:0 u2:0 u4:0 u5:2 u7:0]  D[d3:0 d6:2 d8:1]`
+- up apexes (raw labels) `200020` → canonical `011101`  ·  `A=012121021  U[u0:2 u1:0 u2:0 u4:0 u5:2 u7:0]  D[d3:0 d6:1 d8:2]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `011101`:
+
+- up apexes (raw labels) `200020` → canonical `011101`  ·  `A=012121012  U[u0:2 u1:0 u3:0 u4:0 u6:2 u7:0]  D[d2:0 d5:2 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011101.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011101.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011101.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011101.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011110.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011110.md
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--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011110.md
@@ -0,0 +1,36 @@
+# Up-tooth apex sequence `011110`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 4×colour1.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **5** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_011110.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `011110`:
+
+- up apexes (raw labels) `200002` → canonical `011110`  ·  `A=012121012  U[u0:2 u1:0 u2:0 u3:0 u4:0 u5:2]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `200002` → canonical `011110`  ·  `A=012121021  U[u0:2 u1:0 u2:0 u3:0 u4:0 u5:2]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011110`:
+
+- up apexes (raw labels) `200002` → canonical `011110`  ·  `A=012121012  U[u0:2 u1:0 u2:0 u3:0 u4:0 u6:2]  D[d5:2 d7:0 d8:1]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `011110`:
+
+- up apexes (raw labels) `200002` → canonical `011110`  ·  `A=012121201  U[u0:2 u1:0 u2:0 u3:0 u5:0 u7:2]  D[d4:0 d6:1 d8:2]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `011110`:
+
+- up apexes (raw labels) `200002` → canonical `011110`  ·  `A=012121201  U[u0:2 u1:0 u2:0 u4:0 u5:0 u7:2]  D[d3:0 d6:1 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011110.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011110.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011110.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011110.png
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index 0000000..49911b1
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011202.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011202.md
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index 0000000..5f3f4ea
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011202.md
@@ -0,0 +1,23 @@
+# Up-tooth apex sequence `011202`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **2** of 7 M(T) (dihedral classes).
+- **2** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_011202.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `011202`:
+
+- up apexes (raw labels) `200121` → canonical `011202`  ·  `A=012120102  U[u0:2 u1:0 u2:0 u4:1 u5:2 u7:1]  D[d3:0 d6:2 d8:1]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `011202`:
+
+- up apexes (raw labels) `200121` → canonical `011202`  ·  `A=012120102  U[u0:2 u1:0 u3:0 u4:1 u6:2 u7:1]  D[d2:0 d5:2 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011202.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011202.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011202.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011202.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011220.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011220.md
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index 0000000..2ad69e0
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011220.md
@@ -0,0 +1,29 @@
+# Up-tooth apex sequence `011220`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **3** of 7 M(T) (dihedral classes).
+- **3** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_011220.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `011220`:
+
+- up apexes (raw labels) `200112` → canonical `011220`  ·  `A=012102012  U[u0:2 u1:0 u2:0 u4:1 u5:1 u6:2]  D[d3:2 d7:0 d8:1]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `011220`:
+
+- up apexes (raw labels) `200112` → canonical `011220`  ·  `A=012120201  U[u0:2 u1:0 u2:0 u4:1 u5:1 u7:2]  D[d3:0 d6:1 d8:2]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `011220`:
+
+- up apexes (raw labels) `200112` → canonical `011220`  ·  `A=012120201  U[u0:2 u1:0 u3:0 u4:1 u6:1 u7:2]  D[d2:0 d5:1 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011220.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011220.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011220.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_011220.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012012.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012012.md
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index 0000000..3ff2eb6
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012012.md
@@ -0,0 +1,30 @@
+# Up-tooth apex sequence `012012`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **3** of 7 M(T) (dihedral classes).
+- **4** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_012012.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `012012`:
+
+- up apexes (raw labels) `201201` → canonical `012012`  ·  `A=012012012  U[u0:2 u1:0 u2:1 u3:2 u4:0 u5:1]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201201` → canonical `012012`  ·  `A=012012021  U[u0:2 u1:0 u2:1 u3:2 u4:0 u5:1]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `012012`:
+
+- up apexes (raw labels) `201201` → canonical `012012`  ·  `A=012012021  U[u0:2 u1:0 u2:1 u3:2 u4:0 u6:1]  D[d5:1 d7:0 d8:2]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `012012`:
+
+- up apexes (raw labels) `201201` → canonical `012012`  ·  `A=012012102  U[u0:2 u1:0 u2:1 u3:2 u5:0 u7:1]  D[d4:0 d6:2 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012012.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012012.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012012.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012012.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012021.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012021.md
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index 0000000..9fd3251
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012021.md
@@ -0,0 +1,37 @@
+# Up-tooth apex sequence `012021`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **6** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_012021.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `012021`:
+
+- up apexes (raw labels) `201210` → canonical `012021`  ·  `A=012010212  U[u0:2 u1:0 u2:1 u3:2 u5:1 u6:0]  D[d4:2 d7:0 d8:1]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+3 colouring(s) with up-tooth sequence `012021`:
+
+- up apexes (raw labels) `201210` → canonical `012021`  ·  `A=012010212  U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0]  D[d4:2 d6:0 d8:1]`
+- up apexes (raw labels) `201210` → canonical `012021`  ·  `A=012012012  U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0]  D[d4:0 d6:2 d8:1]`
+- up apexes (raw labels) `201210` → canonical `012021`  ·  `A=012012021  U[u0:2 u1:0 u2:1 u3:2 u5:1 u7:0]  D[d4:0 d6:1 d8:2]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `012021`:
+
+- up apexes (raw labels) `201210` → canonical `012021`  ·  `A=012010212  U[u0:2 u1:0 u2:1 u4:2 u5:1 u6:0]  D[d3:2 d7:0 d8:1]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `012021`:
+
+- up apexes (raw labels) `201210` → canonical `012021`  ·  `A=012010212  U[u0:2 u1:0 u2:1 u4:2 u5:1 u7:0]  D[d3:2 d6:0 d8:1]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012021.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012021.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012021.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012021.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012102.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012102.md
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index 0000000..3196956
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012102.md
@@ -0,0 +1,17 @@
+# Up-tooth apex sequence `012102`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **1** of 7 M(T) (dihedral classes).
+- **1** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_012102.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `012102`:
+
+- up apexes (raw labels) `201021` → canonical `012102`  ·  `A=012021021  U[u0:2 u1:0 u2:1 u4:0 u5:2 u6:1]  D[d3:1 d7:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012102.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012102.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012102.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012102.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012120.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012120.md
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index 0000000..f7f8159
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012120.md
@@ -0,0 +1,23 @@
+# Up-tooth apex sequence `012120`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **2** of 7 M(T) (dihedral classes).
+- **2** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_012120.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `012120`:
+
+- up apexes (raw labels) `201012` → canonical `012120`  ·  `A=012012012  U[u0:2 u1:0 u2:1 u4:0 u5:1 u6:2]  D[d3:2 d7:0 d8:1]`
+
+## G06 — word=UUDUUDUUD bites=-
+
+1 colouring(s) with up-tooth sequence `012120`:
+
+- up apexes (raw labels) `201012` → canonical `012120`  ·  `A=012021201  U[u0:2 u1:0 u3:1 u4:0 u6:1 u7:2]  D[d2:1 d5:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012120.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012120.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012120.png b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012120.png
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012201.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012201.md
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index 0000000..964cd81
--- /dev/null
+++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012201.md
@@ -0,0 +1,37 @@
+# Up-tooth apex sequence `012201`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **4** of 7 M(T) (dihedral classes).
+- **6** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_012201.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G02 — word=UUUUDUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `012201`:
+
+- up apexes (raw labels) `201120` → canonical `012201`  ·  `A=012020121  U[u0:2 u1:0 u2:1 u3:1 u5:2 u6:0]  D[d4:1 d7:0 d8:2]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+3 colouring(s) with up-tooth sequence `012201`:
+
+- up apexes (raw labels) `201120` → canonical `012201`  ·  `A=012020121  U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0]  D[d4:1 d6:0 d8:2]`
+- up apexes (raw labels) `201120` → canonical `012201`  ·  `A=012021012  U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0]  D[d4:0 d6:2 d8:1]`
+- up apexes (raw labels) `201120` → canonical `012201`  ·  `A=012021021  U[u0:2 u1:0 u2:1 u3:1 u5:2 u7:0]  D[d4:0 d6:1 d8:2]`
+
+## G04 — word=UUUDUUUDD bites=-
+
+1 colouring(s) with up-tooth sequence `012201`:
+
+- up apexes (raw labels) `201120` → canonical `012201`  ·  `A=012020121  U[u0:2 u1:0 u2:1 u4:1 u5:2 u6:0]  D[d3:1 d7:0 d8:2]`
+
+## G05 — word=UUUDUUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `012201`:
+
+- up apexes (raw labels) `201120` → canonical `012201`  ·  `A=012020121  U[u0:2 u1:0 u2:1 u4:1 u5:2 u7:0]  D[d3:1 d6:0 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012201.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012201.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012210.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012210.md
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+# Up-tooth apex sequence `012210`
+
+Canonical up-tooth apex colour sequence (read u0 < u1 < ... in cyclic order around A(T), reduced modulo the six colour permutations) for Kempe-balanced 3-colourings of M(T) with **n = 9**, **m = 6 up teeth**.
+
+- Colour multiset: 2×colour0, 2×colour1, 2×colour2.
+- Realised by **3** of 7 M(T) (dihedral classes).
+- **4** Kempe-balanced colourings (mod colour permutation) produce it.
+- Figure: `seq_012210.png` (black rings mark the up-tooth apexes).
+
+Colouring dump key: `A=` annular cycle a0..a_{n-1}; `U[...]` up-tooth apexes; `D[...]` singleton down apexes `d` and bite apexes `p`. Colours are 0/1/2 = 0:orange, 1:blue, 2:green.
+
+## G00 — word=UUUUUUDDD bites=-
+
+2 colouring(s) with up-tooth sequence `012210`:
+
+- up apexes (raw labels) `201102` → canonical `012210`  ·  `A=012021012  U[u0:2 u1:0 u2:1 u3:1 u4:0 u5:2]  D[d6:2 d7:0 d8:1]`
+- up apexes (raw labels) `201102` → canonical `012210`  ·  `A=012021021  U[u0:2 u1:0 u2:1 u3:1 u4:0 u5:2]  D[d6:1 d7:0 d8:2]`
+
+## G01 — word=UUUUUDUDD bites=-
+
+1 colouring(s) with up-tooth sequence `012210`:
+
+- up apexes (raw labels) `201102` → canonical `012210`  ·  `A=012021012  U[u0:2 u1:0 u2:1 u3:1 u4:0 u6:2]  D[d5:2 d7:0 d8:1]`
+
+## G03 — word=UUUUDUDUD bites=-
+
+1 colouring(s) with up-tooth sequence `012210`:
+
+- up apexes (raw labels) `201102` → canonical `012210`  ·  `A=012021201  U[u0:2 u1:0 u2:1 u3:1 u5:0 u7:2]  D[d4:0 d6:1 d8:2]`
+
diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012210.pdf b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/seq_012210.pdf
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diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/summary.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/kempe_up_tooth_sequences_n9_m6/summary.md
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+# Up-tooth apex sequences of Kempe-balanced colourings (n=9, m=6)
+
+Every full medial tire graph M(T) with |A(T)| = 9 and exactly 6 up teeth, one representative per dihedral class: **7 M(T)**. For each we enumerate the Kempe-balanced (valid) proper 3-colourings (modulo colour permutation), read the up-tooth apex colour sequence u0<u1<... in cyclic order, and reduce it modulo colour permutation (NOT dihedral symmetry).
+
+- Total Kempe-balanced colourings (mod colour permutation): **127**.
+- Distinct canonical up-tooth sequences overall: **28**.
+
+## Distinct canonical up-tooth sequences
+
+| sequence | colour multiset | #M(T) realising | #colourings |
+|---|---|---|---|
+| `000000` | 6 | 4 | 5 |
+| `000011` | 4+2 | 7 | 12 |
+| `000101` | 4+2 | 4 | 8 |
+| `000110` | 4+2 | 5 | 7 |
+| `001001` | 4+2 | 2 | 2 |
+| `001010` | 4+2 | 2 | 2 |
+| `001100` | 4+2 | 4 | 6 |
+| `001111` | 4+2 | 5 | 7 |
+| `001122` | 2+2+2 | 5 | 8 |
+| `001212` | 2+2+2 | 3 | 6 |
+| `001221` | 2+2+2 | 4 | 5 |
+| `010001` | 4+2 | 1 | 1 |
+| `010100` | 4+2 | 1 | 1 |
+| `010111` | 4+2 | 1 | 1 |
+| `010221` | 2+2+2 | 1 | 1 |
+| `011000` | 4+2 | 4 | 5 |
+| `011011` | 4+2 | 4 | 6 |
+| `011022` | 2+2+2 | 3 | 4 |
+| `011101` | 4+2 | 4 | 7 |
+| `011110` | 4+2 | 4 | 5 |
+| `011202` | 2+2+2 | 2 | 2 |
+| `011220` | 2+2+2 | 3 | 3 |
+| `012012` | 2+2+2 | 3 | 4 |
+| `012021` | 2+2+2 | 4 | 6 |
+| `012102` | 2+2+2 | 1 | 1 |
+| `012120` | 2+2+2 | 2 | 2 |
+| `012201` | 2+2+2 | 4 | 6 |
+| `012210` | 2+2+2 | 3 | 4 |
+
+Note: every realised sequence has its three colour-counts of **equal parity** — exactly the outer-face Kempe-parity constraint (each colour pair meets the up-tooth apexes an even number of times). With m = 6 up teeth (m is even) every count must be **even**, so the only admissible colour multisets are 2+2+2, 4+2, 6.
+
+## Step 4 — grouping M(T) by their set of unique up-tooth sequences
+
+The 7 M(T) fall into **6** groups by the set of canonical up-tooth sequences they realise:
+
+| #M(T) | set of up-tooth sequences | M(T) ids |
+|---|---|---|
+| 2 | { `000000`, `000011`, `000110`, `001100`, `001111`, `001221`, `011000`, `011022`, `011110`, `012012`, `012210` } | G00, G01 |
+| 1 | { `000000`, `000011`, `000101`, `001100`, `001111`, `001122`, `001212`, `011000`, `011011`, `011022`, `011101`, `012021`, `012201` } | G02 |
+| 1 | { `000011`, `000101`, `000110`, `001122`, `001212`, `001221`, `011011`, `011101`, `011110`, `012012`, `012021`, `012201`, `012210` } | G03 |
+| 1 | { `000000`, `000011`, `000110`, `001001`, `001111`, `001122`, `011000`, `011011`, `011220`, `012021`, `012102`, `012120`, `012201` } | G04 |
+| 1 | { `000011`, `000101`, `001010`, `001100`, `001111`, `001122`, `010001`, `010100`, `010111`, `010221`, `011101`, `011202`, `011220`, `012120` } | G06 |
+| 1 | { `000011`, `000101`, `000110`, `001001`, `001010`, `001122`, `001212`, `001221`, `011011`, `011101`, `011110`, `011202`, `011220`, `012021`, `012201` } | G05 |
+
+## M(T) atlas (ids)
+
+| id | word / bites | #Kempe-balanced | up-tooth sequence set |
+|---|---|---|---|
+| G00 | word=UUUUUUDDD bites=- | 22 | { `000000`, `000011`, `000110`, `001100`, `001111`, `001221`, `011000`, `011022`, `011110`, `012012`, `012210` } |
+| G01 | word=UUUUUDUDD bites=- | 11 | { `000000`, `000011`, `000110`, `001100`, `001111`, `001221`, `011000`, `011022`, `011110`, `012012`, `012210` } |
+| G02 | word=UUUUDUUDD bites=- | 17 | { `000000`, `000011`, `000101`, `001100`, `001111`, `001122`, `001212`, `011000`, `011011`, `011022`, `011101`, `012021`, `012201` } |
+| G03 | word=UUUUDUDUD bites=- | 26 | { `000011`, `000101`, `000110`, `001122`, `001212`, `001221`, `011011`, `011101`, `011110`, `012012`, `012021`, `012201`, `012210` } |
+| G04 | word=UUUDUUUDD bites=- | 13 | { `000000`, `000011`, `000110`, `001001`, `001111`, `001122`, `011000`, `011011`, `011220`, `012021`, `012102`, `012120`, `012201` } |
+| G05 | word=UUUDUUDUD bites=- | 20 | { `000011`, `000101`, `000110`, `001001`, `001010`, `001122`, `001212`, `001221`, `011011`, `011101`, `011110`, `011202`, `011220`, `012021`, `012201` } |
+| G06 | word=UUDUUDUUD bites=- | 18 | { `000011`, `000101`, `001010`, `001100`, `001111`, `001122`, `010001`, `010100`, `010111`, `010221`, `011101`, `011202`, `011220`, `012120` } |
+
+## Per-sequence notes
+
+- [`000000`](seq_000000.md) — figure `seq_000000.png`
+- [`000011`](seq_000011.md) — figure `seq_000011.png`
+- [`000101`](seq_000101.md) — figure `seq_000101.png`
+- [`000110`](seq_000110.md) — figure `seq_000110.png`
+- [`001001`](seq_001001.md) — figure `seq_001001.png`
+- [`001010`](seq_001010.md) — figure `seq_001010.png`
+- [`001100`](seq_001100.md) — figure `seq_001100.png`
+- [`001111`](seq_001111.md) — figure `seq_001111.png`
+- [`001122`](seq_001122.md) — figure `seq_001122.png`
+- [`001212`](seq_001212.md) — figure `seq_001212.png`
+- [`001221`](seq_001221.md) — figure `seq_001221.png`
+- [`010001`](seq_010001.md) — figure `seq_010001.png`
+- [`010100`](seq_010100.md) — figure `seq_010100.png`
+- [`010111`](seq_010111.md) — figure `seq_010111.png`
+- [`010221`](seq_010221.md) — figure `seq_010221.png`
+- [`011000`](seq_011000.md) — figure `seq_011000.png`
+- [`011011`](seq_011011.md) — figure `seq_011011.png`
+- [`011022`](seq_011022.md) — figure `seq_011022.png`
+- [`011101`](seq_011101.md) — figure `seq_011101.png`
+- [`011110`](seq_011110.md) — figure `seq_011110.png`
+- [`011202`](seq_011202.md) — figure `seq_011202.png`
+- [`011220`](seq_011220.md) — figure `seq_011220.png`
+- [`012012`](seq_012012.md) — figure `seq_012012.png`
+- [`012021`](seq_012021.md) — figure `seq_012021.png`
+- [`012102`](seq_012102.md) — figure `seq_012102.png`
+- [`012120`](seq_012120.md) — figure `seq_012120.png`
+- [`012201`](seq_012201.md) — figure `seq_012201.png`
+- [`012210`](seq_012210.md) — figure `seq_012210.png`
+