didericis
984655fd3d
Backward bridge-switch search (sharded over valid parity partitions) found an Even Level Graph witness for each of the four previously-open duals: dual 0: partition 12, witness orbit 9458 dual 3: partition 9, witness orbit 388 dual 4: partition 23, witness orbit 3842 dual 5: partition 12, witness orbit 165668 So all four are bridge-derived level graphs, hence valid derived level graphs. Combined with the two duals that are Even Level Graphs outright, the disjunction is now confirmed for ALL SIX critical iso classes at n=21 -- the first nontrivial test of the conjecture passes. Why it worked where exhaustion failed: a witness, when it exists, tends to sit in a SMALL orbit (here a few hundred to ~1.7e5 states) reachable quickly, while other parity partitions of the same triangulation have orbits >1e6. We only need one good partition. The bridge restriction both shrinks orbits ~100x and guarantees validity, so any ELG found in a backward orbit is an immediate witness. - Update paper n=21 subsection to report the resolution. - Add shard_hunt.py (partition-sharded parallel witness hunt). Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
54 lines
5.6 KiB
TeX
54 lines
5.6 KiB
TeX
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