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OPE-3: n-queens fresh Scout dossier + Level B statement pin (board-named) - #3

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Summary

  • Fresh feasibility dossier for n-queens as a board-named, full-process run (parent OPE-2). Five readings disambiguated on docs/FEASIBILITY_RUBRIC.md: (a) existence iff n≠2,3 — 88, TARGET; (b) counting Q(n) 54; (c) Simkin asymptotics 28; (d) completion NP-complete 36; (e) toroidal Pólya 80 (different theorem, out of scope).
  • Level B statement pin in catalog/problems/n-queens/STATEMENT.md: NonAttacking (q : Fin n → Fin n) = injective + both subtraction-free diagonal families; theorem n_queens_exists_iff (n : ℕ) : (∃ q, NonAttacking q) ↔ (n ≠ 2 ∧ n ≠ 3); n=0 convention stated; what-counts-as-done + out-of-scope list.
  • Novelty pre-screen against the local Mathlib pin a719ba5c31 (v4.10.0): ZERO named n-queens theorem (commands + hit list in DOSSIER.json). Literature: Pauls 1874; Hoffman–Loessi–Moore 1969; Bernhardsson 1991; Bell–Stevens 2009. "Gauss 1850" corrected to the 8×8 count only.
  • Catalog row → shortlisted (PR OPE-1424: n-queens Level A (n=2 none / n=3 none / n=4 [1,3,0,2]) Paul3435/open-math-lab#174 Level A history kept in tickets/artifacts/prior_art); ledger update block + table row; mathforge score n-queens run (problems/n-queens/feasibility.json).

Paperclip

  • Issue: OPE-3 (parent OPE-2)
  • Agent role: Scout

Math honesty

  • Claim status: none. Known-classical theorem; formalize-only. No Lean opened, nothing solved.
  • ProofLab/NQueens.lean (PR OPE-1424: n-queens Level A (n=2 none / n=3 none / n=4 [1,3,0,2]) Paul3435/open-math-lab#174) is cited as prior art / reusable encoding, not as a solution; the namesake was left residual there.
  • Scout brute-force checked the transcribed Bernhardsson construction for n = 4..199 (0 failures) — a transcription sanity check, not a proof.
  • Residual risks: R1 n=0 convention; R2 both diagonal families load-bearing, subtraction-free encoding equivalence to be reviewed; R3 1-indexed literature vs 0-indexed Fin + the n mod 6 ∈ {2,3} list surgery.

Test plan

  • python3 test_mathforge.py -v — 11 tests OK
  • python3 bin/mathforge status
  • JSON parse of catalog/problems.json + DOSSIER.json
  • (no Lean in this PR)

Board

  • Please review + merge if OK
  • Do not treat this PR as external publication of a proof

… pin

- Disambiguate five "n-queens" readings on the feasibility rubric; target (a)
  existence iff n≠2,3 scores 88; expected known-classical, formalize-only
- Pin Lean-shaped statement: NonAttacking (Fin n → Fin n, injective + both
  subtraction-free diagonal families) and n_queens_exists_iff; n=0 convention
- Novelty pre-screen: local Mathlib a719ba5c31 (v4.10.0) grep, ZERO named
  n-queens theorem; literature handles Pauls 1874 / HLM 1969 / Bernhardsson
  1991 / Bell–Stevens 2009; PR Paul3435#174 Level A cited as prior art, not solution
- Catalog row → shortlisted; ledger block + table row; mathforge score run
- Verify: python3 test_mathforge.py (11 OK); python3 bin/mathforge status
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