openresearch
5c01ec43ea
docs: sofa × HN — combined stress test framing
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The key insight: standalone they are insanely hard, together they
either melt the model or reveal structure. This is better than 3-SAT
because both components are unsolved — any result is novel.
Combined: sofa navigates corridor (continuous) AND at each step,
occupied positions form a valid unit-distance coloring (discrete).
This is the matter→light move at its deepest.
2026-07-03 23:46:25 +00:00
openresearch
4c47fe4e43
docs: moving sofa × Hadwiger-Nelson as next octagon test case
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Two unsolved geometric problems as a combined octagon test:
1. Moving Sofa (Moser 1966): max-area shape navigating L-corridor.
Unsolved. Best: Gerver 2.2195. Upper: 2.8284.
Reformulated as: corridor graph + admissible subsets = coloring.
2. Hadwiger-Nelson (1950): chromatic number of the plane.
Unsolved. Known: 5 ≤ χ(ℝ²) ≤ 7. de Grey (2018): 5-chromatic graph.
Already has spectral structure: Hoffman bound χ ≥ λ_max + 1.
The connection: both are geometric constraint satisfaction.
- Sofa: which shapes satisfy the corridor constraint?
- HN: which colorings satisfy the unit-distance constraint?
- Reformulation: sofa = corridor coloring, HN = plane coloring.
Pipeline connection: COUCH gate in GCCL.lean already references this.
'Apartment constraint' = sofa-in-corridor. FYC gate = rejects
impossible traversal = rejects shapes that can't make the turn.
Experiment:
1. Discretize corridor → graph → adjacency matrix → spectrum
2. Test known sofa shapes (Gerver, Hammersley) for spectral
distinguishability
3. Build de Grey's 5-chromatic graph → compute Hoffman bound
4. Is the bound tight (λ_max+1=5)? Or loose?
Priority: BETTER than 3-SAT because the sofa is unsolved (spectral
shortcut = real result) and HN already has spectral structure
(measure how tight). Different problem class (geometric optimization)
from previous tests (combinatorial, number-theoretic, structural).
Effort: 6-12 hours Python+numpy, no GPU needed.
2026-07-03 23:36:29 +00:00
