Issue 112 retrieval: RW/BBW finite criterion vs exact wrapping/M tables (Phase 0)

[LightChainr]

Closes nothing; addresses the re-queued Phase 0 retrieval slice of #112 (parent stays open).

Scope

Retrieval/feasibility only — no production implementation, no new Monte Carlo, no #636, no STATUS edit. One notes file + references.bib gap-fill.

Deliverable

notes/rw-bbw-vs-wrapping-tables-20260908.md answers the five issue questions with verbatim primary-source quotes:

1. Q1 (criterion): Riordan–Walters 2007 = BBW 1-independent renormalization, applies directly to square-site. Lemma 1 quoted: p0 = 0.8639; modernized by BJSS 2022 Theorem 1.3 p_max(Z^2) <= 0.8457 (verified verbatim from arXiv HTML v2).
2. Q2 (events/thresholds): open-boundary 2s x s unique-largest-cluster block event (quoted), strict P_p(E_e) > 0.8457, exact binomial tail at per-run alpha 1/6000000; 2007 N=400/M>=378 tail quoted and reproduced exactly by the merged gate.
3. Q3 (our engines): the repo's exact torus wrapping/M tables (L<=4) and literature estimator tables (n<=24) are the wrong observable family — periodic/global vs open-boundary/local; no identity connects them. The valid estimators already exist on main from PRs Add a certified finite-size pc feasibility gate #278–Freeze pc confidence preregistration and ledger audit #281 (exact Fraction oracle, O(s^2) evaluator, pre-registration ledger). Nonmonotonicity caveat from Freeze tiny open-boundary pc block-event semantics #279 carried forward.
4. Q4 (size/count): statistical power is not binding (0.95 at pi=0.95 with N=400); geometry is. RW 2007 published square-site [0.5925,0.5930]; heuristic s^-3/4 law gives ~8.6x linear / ~73x area for width 1e-4. Any achievable interval is dominated by existing 9–10-digit estimates — no scientific improvement on offer.
5. Q5 (deterministic?): No — exact enumeration is impractical past s=2 (RW's own quote: "Needless to say, this is impractical"); transfer-matrix is exponential in width; RW quote the RNG assumption explicitly. Output is necessarily a rigorous CI conditional on genuine IID trials.

Outcome

Methodologically interesting but weak (matches the #278 classification). Recommendation: keep #112 parked; the only unmerged work is the #278 production gate (exploratory placement + one fresh pre-registered run), not justified now.

References

Adds the three missing bibtex entries: RiordanWalters2007RigorousCI (primary read from arXiv PDF 2026-09-08), BalisterBollobasWalters2012OneIndependent (bibliographic data from Cambridge Core; full text NOT FOUND/unchecked this session), BalisterJohnstonSaveryScott2022Improved (primary read from arXiv HTML v2).

Verification

• 2007 legacy tail reproduced independently (float): 1.1489903528940095e-07 vs published 1.1489···e-7; modern cutoffs 373/372 tails agree with the merged exact-Fraction gate to float precision.
• scripts/rigorous_pc_confidence_gate.py runs clean on the current tree.

[LightChainr]

Verification comment, not a merge request. Ticket stays open.

Phase 0 as assigned: notes + bib, no production, no new MC, no STATUS, no #636. Five questions each have a carrier.

Keep:

• Criterion is RW 2007 / BBW 1-independent renormalization; modern cut p_max(Z^2) ≤ 0.8457 (BJSS) replaces 0.8639.
• Required event is open-boundary unique-largest-cluster on 2s×s, not torus wrapping/M. Exact L≤4 wrapping tables cannot feed the certificate — wrong observable, wrong boundary.
• Outcome methodologically interesting but weak: machinery already on main (Add a certified finite-size pc feasibility gate #278–Freeze pc confidence preregistration and ledger audit #281); any rerun is scientifically dominated by 9–10 digit estimates; exact enum dies past s=2. Do not open a production run from this PR.

Caveat: BBW 2012 full text is marked NOT FOUND this session (Cambridge Core bibliographic only). The usable quotes are RW 2007 and BJSS 2022, which is enough for Phase 0.

Do not close #112.