Move root experiment scripts into their papers' experiments/ folders

Relocate the standalone Python scripts from the repo root into the
experiments/ folder of the paper each one belongs to:

  plane_depth_sequencing/experiments/
    plane_depth_sequencing.py, draw_quad_sequence.py,
    draw_quad_sequence_diagram.py, extract_sequence.py,
    plane_depth_sequencing_figure.py, quad_sequence_coloring_check.py
  colored_edge_flip_classes/experiments/   colored_edge_flip_class_survey.py
  colored_pentagon_contractions/experiments/ colored_pentagon_contractions.py
  plane_diamond_coloring/experiments/       plane_diamond_coloring.py

Each file that imports lib.* (still in the repo root) or the sibling
plane_depth_sequencing module gets a sys.path shim that prepends the
repo root (computed three levels up) and, where needed, its own dir.
Imports verified to resolve from a neutral working directory.

flip_symmetric_census.py is intentionally left in the root.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

papers/plane_depth_sequencing/experiments/plane_depth_sequencing.py

@@ -1,4 +1,6 @@
 """Plane depth sequencing on maximal planar graphs."""
+import os, sys
+sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), "..", "..", "..")))  # repo root for `lib`
 import random
 from typing import Any, TypedDict
 from sage.all import Graph, graphs  # type: ignore[attr-defined]  # pylint: disable=no-name-in-module
@@ -160,9 +162,11 @@ def extended_deep_embedding(
             next_vertex += 1
             g_prime.add_vertex(x)
             g_prime.add_edges([(x, a), (x, b), (x, c)])
-            depth_labelling[x] = depth_labelling[a] + 1
             if frozenset(face_vertices) == outer_vertices:
                 outer_cap_vertex = x
+                depth_labelling[x] = -1  # Outer-cap vertex has depth -1
+            else:
+                depth_labelling[x] = depth_labelling[a] + 1
 
     g_prime.is_planar(set_embedding=True)
     embedding = g_prime.get_embedding()