[issue576] Ground the wrapping channel on published closed forms

[LightChainr]

Issue #576 — put the wrapping channel on published ground

Part 1 — Akhunzhanov–Eserkepov–Tarasevich exact torus polynomials (VALIDATED, discrepancies resolved)

Retrieved torus.txt from the arXiv ancillary (https://arxiv.org/src/2204.01517v1/anc/torus.txt; J. Phys. A 55, 204004 (2022), arXiv:2204.01517). The paper covers NN square site torus wrapping only — it does NOT handle NN+NNN (Sq8) matching, so only the main channel is validated.

Two independent exact enumerations (L=2..5, full polynomials):

• doubled-grid criterion (exact_wrapping_enum.cpp): 7, 175, 19571, 8853291
• displacement-union-find (exact_wrapping_enum2.cpp): 7, 175, 19571, 8853301

Resolution of the earlier L=5 "diff 10": the same-row doubled-grid criterion is not equivalent to winding — it misses spiral configurations (cluster winds x AND y; the lift to the doubled strip has no same-row (r,0),(r,L) pair). A full 2^25 scan (exact_wrapping_criterion_diff.cpp) finds exactly 10 such configs, all in the c_15 bin, each verified to wind both ways. The published polynomial is correct (per-coefficient match at L=3,4,5); the first enumerator was wrong.

Retraction: the earlier "L≥9 blocks appear corrupted" claim compared P_L(1/2) to 0.1694 — a category error (P_L(1/2) → 0 since p=1/2 < p_c; 0.1694 is the critical continuum π({1,0})(i)). Correct anchor: P_L(p_c) → R^v = 0.521058290… (Mertens–Ziff). Every block L=3..12 passes the paper's proven divisibility test (c_k ≡ 0 mod L²/gcd(k,L²)), and P_L(p_c) converges smoothly/monotonically to 0.521058… (L=3: 0.521274, L=12: 0.519931). The only genuine file defect is the L=10 block truncated at 100 of 101 coefficients — the missing trailing coefficient is necessarily c_100 = 1.

Part 2 — Pinson/Arguin continuum wrapping at r = 1,2,4 (recomputed)

Direct Gaussian sum vs theta form agree to ~1e-110…1e-116 at 100 dps:

• π({1,0})(i) = 0.16941543532134688938260796919875445000145337645375
• π({1,0})(2i) = 0.50303589769463904028462207879367242007166407775608
• π({1,0})(4i) = 0.85596932105387227330836216781610004621209130143655
• ratios to r=1: 2.9692447842221780796 (r=2), 5.0524872154079183417 (r=4)

Cross-check: Pruessner–Moloney (cond-mat/0310361) report agreement with Pinson at r=2 to < 1e-8.

Decision: (ii) explicit non-claim. The freeze file should declare the matching-odd slope is NOT claimed to be the Pinson wrapping; these three numbers are named non-claims (continuum primal Q=1 FK class probabilities, not finite-lattice matching data).

Part 3 — three distinct 11/4 objects (disambiguated, no claim-ledger entry)

• Ê4(2i)/Ê4(i) = 11/4 — modular weight-4 amplitude ratio (staircase competitor)
• Newman–Ziff L^{-11/4} — finite-size convergence rate (1/ν+θ = 3/4+2)
• Mertens–Ziff matching root ~ L^{-4} — a third, different exponent

Files (no existing files modified; additions only)

• notes/issue576-wrapping-grounding.md (updated with resolution pass)
• scripts/exact_wrapping_enum.cpp, exact_wrapping_enum2.cpp, exact_wrapping_criterion_diff.cpp, torus_wrapping_polynomial_check.py, gen_issue576_derived.py, gen_issue576_resolution.py
• results/issue576/wrapping-grounding/{REPORT.md,metadata.json,commands.txt,raw/torus.txt,derived/*}

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