From 6f0d036e44a0a2c17e477343fa6ffa4e49e87b5a Mon Sep 17 00:00:00 2001 From: didericis Date: Fri, 22 May 2026 11:05:04 -0400 Subject: [PATCH] Restate conjecture with "bridge-derived"; update empirical table and n=21 - Conjecture now reads "bridge-derived level graph ... an intertwining tree, or both" -- the stronger form the evidence actually supports (a bridge- derived level graph is automatically a valid derived level graph). - Empirical table recomputed for bridge-derivability, exhaustively for n<=9 (every backward bridge-orbit fully enumerable there): n=7: 1 inter-only; n=8: 2 inter-only; n=9: 14 inter-only; missing=0. Added prose: below n=21 every class is intertwining, so the table shows how far the bridge-derived disjunct reaches on its own (36/50 at n=9) and that the two disjuncts complement each other; "bridge only" is 0 in range. - n=21 subsection notes the four witnesses are explicit, short (path lengths 3,1,2,4), archived, and step-verified. Co-Authored-By: Claude Opus 4.7 --- .../experiments/recompute_table.py | 37 ++++++++++++++ papers/even_level_graph_generators/paper.pdf | Bin 549382 -> 550765 bytes papers/even_level_graph_generators/paper.tex | 48 +++++++++++++----- 3 files changed, 71 insertions(+), 14 deletions(-) create mode 100644 papers/even_level_graph_generators/experiments/recompute_table.py diff --git a/papers/even_level_graph_generators/experiments/recompute_table.py b/papers/even_level_graph_generators/experiments/recompute_table.py new file mode 100644 index 0000000..5e40cc7 --- /dev/null +++ b/papers/even_level_graph_generators/experiments/recompute_table.py @@ -0,0 +1,37 @@ +"""Recompute the empirical table for the bridge-derived disjunction: +for each n, count iso classes that are bridge-derived only / intertwining +only / both / neither (missing).""" +import sys +import os +sys.path.insert(0, '/Users/didericis/Code/math-research/papers/' + 'level_resolutions_of_maximal_planar_graphs/experiments') +sys.path.insert(0, os.path.dirname(os.path.abspath(__file__))) +from triangulation_gen import enumerate_all_triangulations +from small_n_probe import is_bridge_derived +from test_disjunction import is_intertwining_tree + + +def main(ns): + print('n iso bridge_only inter_only both missing', flush=True) + for n in ns: + tris = enumerate_all_triangulations(n) + bo = io = both = miss = 0 + for G in tris: + bd = is_bridge_derived(G) + it = is_intertwining_tree(G) + if isinstance(it, tuple): + it = it[0] + if bd and it: + both += 1 + elif bd: + bo += 1 + elif it: + io += 1 + else: + miss += 1 + print(f'{n} {len(tris)} {bo} {io} {both} {miss}', flush=True) + + +if __name__ == '__main__': + ns = [int(x) for x in sys.argv[1:]] or [6, 7, 8, 9, 10, 11, 12] + main(ns) diff --git a/papers/even_level_graph_generators/paper.pdf b/papers/even_level_graph_generators/paper.pdf index 7b8543f14f285a2626acda434758786cc6ac4faa..1b5d0559e462e8b1643de069bbdf97203d058756 100644 GIT binary patch delta 21212 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