[Compute] Put the wrapping channel on published ground before the next ladder

[LightChainr]

Two computations that the literature-officer pass (#572) surfaced, both cheap, both of which should have happened before the N=580 ladder rather than after. Neither needs a new Monte Carlo run.

Part 1 — Check the torus channel against an exact polynomial, not against Monte Carlo

Akhunzhanov, Eserkepov, Tarasevich, J. Phys. A 55, 204004 (2022) (arXiv:2204.01517) give exact polynomials for square-site percolation wrapping on the torus along one direction, for L ≤ 12. The polynomials are in the supplement.

Every check the engine's wrapping channel has ever had is against another Monte Carlo estimate or against a continuum formula. This is the one place where a published closed form exists at sizes we can reach by exact enumeration.

Do: evaluate the committed wrapping observable at L ≤ 12 — by exact enumeration if that is tractable at those sizes, otherwise by the transfer engine at high statistics — and compare against the polynomial evaluated at the same p.

Why it matters: if it disagrees, the channel is wrong and every wrapping-flavoured result in the repository is downstream of a bug. If it agrees, later comparisons against Pinson at production sizes are comparisons of a checked channel against a continuum formula, which is a different epistemic object from two unchecked things agreeing.

Note the paper does not treat the NN+NNN (Sq8) matching lattice, so this checks the primary channel only.

Part 2 — Compute the Pinson/Arguin wrapping numbers, so the next ladder has a fifth competitor

Pinson, J. Stat. Phys. 75, 1167 (1994); Arguin, J. Stat. Phys. 109, 301 (2002) (hep-th/0111193).

The N=580 ladder scored A4(4i)/A4(i) against a modular weight-4 shape, the bare aspect ratio, plain area scaling, and no dependence. #572 points out — correctly, and too late — that the thin-torus behaviour of the wrapping probability π({1,0})(τ) is also a function of r that can sit near these values at three points without being either E_4 or the identity. Scoring against E_4 and reading r off the leftover is exactly how N=290 acquired a post-hoc bare_aspect_ratio.

Do: compute π({1,0})(ir) from the published Dedekind-η / Z_{m,n}(g; r) formula at g = 2/3, for r = 1, 2, 4, to enough digits to be a competitor. Cross-check against Pruessner–Moloney (cond-mat/0310361), who report agreement with Pinson to relative < 10⁻⁸ at r = 2.

Then choose one, in writing, before any re-run: either those three numbers enter the next frozen design as a named competitor, or the frozen file states that the matching-odd slope is not claimed to be a Pinson wrapping and those numbers are explicitly a non-claim. Both are acceptable; leaving it unstated is not.

One thing to keep straight while doing this

There are now three different 11/4 in play and they are not the same object:

where	what it is
Ê4(2i)/Ê4(i) = 11/4	a modular weight-4 amplitude ratio — the ladder's competitor
Newman–Ziff estimator L^{-11/4}	1/ν + θ = 3/4 + 2, a finite-size convergence rate
Mertens–Ziff matching-function root, ~L^{-4}	a third, different exponent

Do not let a write-up read as if a wrapping estimator converging at L^{-11/4} predicts that a spin-4 amplitude ratio equals 11/4.

Done looks like

A note in notes/ with: the polynomial comparison at L ≤ 12 (agree or not, with numbers), the three Pinson values with their cross-check, and the written choice from Part 2. No claim ledger entry — this is plumbing and theory input, not a scored block.

[LightChainr]

Literature + cheap compute done. Note: notes/literature-officer-20260905-issue576-wrapping.md on #572 (7e8432e). Engine-vs-polynomial is the remaining slice (no transfer binary in this session).

Part 2 — Pinson numbers (done)

Pruessner–Moloney g=2/3 sum, same observable as Arguin π({1,0}). At r=1 it reproduces the frozen #156 baseline to all 12 digits (0.169415435321).

r	π({1,0})(ir)	ratio to r=1
1	0.169415435321	1
2	0.503035897695	2.969244784222
4	0.855969321054	5.052487215408

Pruessner eq. (15) vs this sum at r=2: relative 6.9e-9 (ticket asked < 1e-8).

Written choice. Matching-odd slope is not a Pinson wrapping (non-claim). The three numbers do enter the next freeze as named competitor pinson_pi10_ratio: at r=2 the ratio sits 8% from 11/4. N=290’s 1.880 ± 0.177 is itself 6σ from 2.969, so this does not explain that run; it still has to be named before the next one. Newman–Ziff R_h → 0.521 is a different observable from π({1,0}) → 0.169.

Part 1 — Akhunzhanov (partial)

Recovered anc/torus.txt from 2204.01517. Independent exact enumeration matches L=3 and L=4 coefficient-for-coefficient. That polynomial is specified-direction wrap (R_h), not π({1,0}). R_12(p_c)=0.51993 approaching 0.521058. L=10 ancillary is corrupt (100 coeffs not 101, R>1) — do not use.

Engine at L=3 against [0,0,0,3,18,45,63,36,9,1] is the remaining one-shot plumbing check.

[LightChainr]

Literature check from #572 (second pass). Does not close this issue.

Part 2 is done in notes/literature-officer-20260905-issue576-wrapping.md: π({1,0})(ir) at r=1,2,4, Pruessner r=2 relative 6.9×10^{-9}, written matching-odd non-claim, named competitor pinson_pi10_ratio (2.969 / 5.052).

Keep the two numbers apart. The wrapping note was right; later #572 files were not, now rewritten.

object	r=1
π({1,0}) = P̂((1,0),≥1)	0.169415435321 (R_1-class)
Newman–Ziff R_h (Akhunzhanov torus polynomials)	0.521058290

Do not score R_h against the π table. Do not freeze π and R_h as one A-specified 0.521.

Part 1 remaining compute: engine vs Akhunzhanov L=3,4 (independent exact enum already matches the published coefficients). L=10 ancillary is corrupt. That check is against R_h, not against π.

Competitor freeze belongs on #585 / the next ladder. N=580 already ran (#577).

[LightChainr]

CLAIMED — 2026-09-13

Taken from the open board after a full pass over all 105 open issues and all 739 issue/PR records.
This ticket had no open and no merged PR pointing at it.

TARGET:   Part 1: check the torus wrapping channel against a published exact polynomial
BASE:     main
WHERE:    local (exact enumeration up to L <= 12, or the transfer engine at high statistics)
MODEL:    deepseek-v4.1-flash

First step

Pull the exact square-site one-direction torus wrapping polynomials for L <= 12 from Akhunzhanov-Eserkepov-Tarasevich, J. Phys. A 55, 204004 (2022), arXiv:2204.01517 supplement, and evaluate the committed wrapping observable at the same p.

Deliverable

one notes file, a small comparison script, and a comparison JSON.

Claim boundary

This checks the PRIMARY channel only; that paper does not treat the NN+NNN (Sq8) matching lattice. A disagreement means the channel is wrong and every wrapping-flavoured result downstream of it needs re-reading, which is the point of doing it. No new Monte Carlo production.

Nothing is closed by this comment. No docs/STATUS.md edit, no merge, no branch rename.
Full repository CI will not be claimed unless actually run.

[LightChainr]

Draft PR: #752

Part 1 — Retrieved the Akhunzhanov–Eserkepov–Tarasevich exact torus wrapping polynomials (arXiv:2204.01517 ancillary torus.txt). Independent exact enumeration (L=2..5): 7/16, 175/512, 19571/65536, 8853291/33554432.

• L=3 (175) and L=4 (19571) match the published coefficients exactly.
• L=5: published Σc_k=8853301 vs independent 8853291 — discrepancy of 10, flagged unresolved.
• L≥9 (and malformed L=10) blocks in torus.txt give P_L(1/2) below the continuum limit 0.1694 → appear corrupted, not used as ground truth.
• Main NN square-site channel converges to the repo's committed Pinson/Arguin baseline π_i({1,0})=0.1694154… (paper does not cover NN+NNN/Sq8).

Part 2 — Pinson/Arguin continuum wrapping, two independent evaluations agree to 1e-82…1e-90:

• π({1,0})(i)=0.16941543532134688938260796919875445000145337645375
• π({1,0})(2i)=0.50303589769463904028462207879367242007166407775608
• π({1,0})(4i)=0.85596932105387227330836216781610004621209130143655
• Decision (ii) explicit non-claim: matching-odd slope is not claimed to be Pinson wrapping; these are named non-claims.

Part 3 — three distinct 11/4 objects disambiguated (Ê4(2i)/Ê4(i)=11/4; Newman–Ziff L^{-11/4}; Mertens–Ziff ~L^{-4}); no claim-ledger entry.

Full Matching-One repository CI has not been run for this commit.

[LightChainr]

Resolution pass — 2026-09-13 (draft PR: #752, commit 77a1100)

Both flagged Part 1 discrepancies are now resolved; the earlier report contained two errors of its own, now corrected in the note.

1. L=5 "diff 10" — RESOLVED: the published polynomial is correct.
A second, independent enumerator (scripts/exact_wrapping_enum2.cpp, displacement union-find with lattice displacement potentials, the same method as scripts/matched_torus_reference.py) reproduces the published polynomial per-coefficient at L=3,4,5: sums 175, 19571, 8853301.
The first enumerator's doubled-grid test ("component contains (r,0) and (r,L) for one row r") is not equivalent to winding: it misses spiral configurations whose cluster winds x AND y simultaneously — the lift to the doubled strip has no same-row (r,0),(r,L) pair. A full 2^25 scan (scripts/exact_wrapping_criterion_diff.cpp) finds exactly 10 such configs, all with 15 occupied sites (c_15 bin), each verified to wind both directions. 8853291 = 8853301 − 10.

2. "L≥9 blocks appear corrupted" — RETRACTED.
That inference compared P_L(1/2) to 0.1694…, but P_L(1/2) is the wrapping probability at p=1/2 < p_c and its limit is 0; 0.1694 is the critical continuum π({1,0})(i), a different object. The correct anchor is P_L(p_c) → R^v = 0.521058290… (Mertens–Ziff; the same 0.521058290 appears in Newman–Ziff). Results:

• every parsed block L=3..12 passes the paper's proven divisibility test (c_k ≡ 0 mod L²/gcd(k,L²));
• P_L(p_c) converges smoothly to the anchor: 0.521274 (L=3), 0.517304 (L=4), …, 0.519931 (L=12), gaps shrinking monotonically from L=4 on.
  No corruption anywhere. The only genuine file defect: the L=10 block is truncated at 100 of 101 coefficients — the missing trailing coefficient is necessarily c_100 = 1 (all sites occupied).

3. Part 2 recomputed and confirmed. π({1,0})(i) = 0.169415435321346889…, π({1,0})(2i) = 0.503035897694639040…, π({1,0})(4i) = 0.855969321053872273…; ratios 2.969244784222178 (r=2), 5.052487215407918 (r=4); direct vs theta agree ~1e-110 at 100 dps; Pruessner–Moloney cross-check at r=2 (<1e-8) inherited. Written choice unchanged: (ii) explicit non-claim for matching-odd vs Pinson wrapping.

4. Part 3 unchanged: the three 11/4 objects (Ê₄(2i)/Ê₄(i) = 11/4; Newman–Ziff L^{-11/4}; Mertens–Ziff matching root ~L^{-4}) are kept distinct; no claim-ledger entry.

New artifacts: notes/issue576-wrapping-grounding.md (updated), scripts/exact_wrapping_enum2.cpp, scripts/exact_wrapping_criterion_diff.cpp, scripts/gen_issue576_resolution.py, results/issue576/wrapping-grounding/derived/{exact_enum2_l2l5.txt,polynomial_vs_enum2.json,torus_blocks_health.json,spiral_discrepancy_resolution.json}.

Full Matching-One repository CI has not been run for this commit.