residue_phase_sweep.py exhaustively enumerates the two colouring control knobs
-- the per-annulus tread phase {0,1}^A and the root-DFS colour order perms(0,1,2)
-- on top of every insertion-site combo, for the graphs the random-phase site
sweep still fails. canonical_coloring_explicit makes this deterministic.
Result (residue_phase_sweep_results.txt): the two hub graphs are RESCUED once
phase is enumerated rather than sampled (so the random-phase fail count overstates
difficulty); the genuine obstructions that survive sites x phases x colour-orders
are exactly the face-leaf graphs (terminal-triangle leaf gadget). Smallest is
seed2 #26 [3,6,3] face (1 combo, 24 settings, all fail at gadget-removal) -- a
minimal obstruction target. Caveat: try_establish is a bounded local Kempe search,
so STILL FAILS means unreachable by the bounded search from canonical-even over
all knob settings, not that no Kempe path exists.
Findings note updated.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
didericis
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