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openresearch 4c47fe4e43 docs: moving sofa × Hadwiger-Nelson as next octagon test case 
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
..
COUCH_COLORING_TARGET.md docs: moving sofa × Hadwiger-Nelson as next octagon test case 2026-07-03 23:36:29 +00:00
DIRECTION_LOG.md docs: record prime-Sidon honest negative (0/35 after Bonferroni) 2026-07-03 23:29:46 +00:00
MILESTONES.md docs: create living targets folder for rapidly evolving goals 2026-07-03 22:13:45 +00:00
OPEN_QUESTIONS.md docs: create living targets folder for rapidly evolving goals 2026-07-03 22:13:45 +00:00
PROJECT_MAP.md docs: create living targets folder for rapidly evolving goals 2026-07-03 22:13:45 +00:00
README.md docs: create living targets folder for rapidly evolving goals 2026-07-03 22:13:45 +00:00
TARGETS.md docs: record prime-Sidon honest negative (0/35 after Bonferroni) 2026-07-03 23:29:46 +00:00

README.md

Living Documents

This folder is for rapidly evolving goals, targets, and project maps.

Unlike the formal docs in docs/research/ (which are measured, stable findings), the documents here change daily. They represent the current direction of the project — what we're aiming at today, which may shift tomorrow.

Document Types

Type Purpose Update frequency
TARGETS.md Current research targets and their status Daily
PROJECT_MAP.md What the project IS right now (not what it was) Daily
MILESTONES.md Near-term milestones with success criteria Weekly
OPEN_QUESTIONS.md Questions we haven't answered yet As needed
DIRECTION_LOG.md Why the direction changed (decision log) On change

Rules

  1. No measurement required here. These are goals, not findings. Findings go in docs/research/ with bytes behind them.
  2. Overwrite freely. The old version is in git history. Don't append — replace.
  3. One sentence per target. If you can't state it in one sentence, it's not a target yet, it's a question.
  4. Link to findings. Each target should link to the relevant docs/research/ document that backs (or refutes) it.
  5. Honesty tag. Each target gets: MEASURED (backed by data), OPEN (untested), or SPECULATIVE (no data yet).

Current Documents