[issue576] Ground the wrapping channel on published closed forms

notes/issue576-wrapping-grounding.md

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+# Issue #576 — Put the wrapping channel on published ground before the next ladder
+
+Branch: `compute/p576-wrapping-channel-grounding-20260913`
+Caller: compute1; resolution pass 2026-09-13 by compute1-retry (second
+independent enumerator, spiral-bug diagnosis, divisibility + P_L(p_c) block
+health, Pinson values recomputed)
+
+This note covers the three parts of the ticket: (1) validate the main wrapping
+channel against the Akhunzhanov–Eserkepov–Tarasevich exact torus polynomials;
+(2) compute the Pinson/Arguin continuum wrapping at `r = 1,2,4` and make the
+either/or declaration; (3) disambiguate the three distinct `11/4` objects.
+
+## Part 1 — Akhunzhanov–Eserkepov–Tarasevich exact torus wrapping polynomials
+
+### Retrieval (attempt record — honest)
+- Paper: R. K. Akhunzhanov, A. V. Eserkepov, Y. Yu. Tarasevich, *Exact
+  percolation probabilities for a square lattice: Site percolation on a plane,
+  cylinder, and torus*, J. Phys. A 55, 204004 (2022), arXiv:2204.01517.
+- The wrapping polynomials are in the arXiv **ancillary** file `torus.txt`.
+- URLs tried (Bash `curl` + WebFetch):
+  - `https://arxiv.org/abs/2204.01517` — confirms a supplement exists; rendered
+    text gives no direct download link.
+  - `https://arxiv.org/src/2204.01517v1/anc/` — ancillary listing; found
+    `torus.txt`, `cylinder.txt`, `Algorithm2.pdf`.
+  - `https://arxiv.org/src/2204.01517v1/anc/torus.txt` — **retrieved
+    successfully** (12,665 bytes; copied to
+    `results/issue576/wrapping-grounding/raw/torus.txt`).
+  - IOPscience article page and the arXiv HTML version — no separately
+    downloadable polynomial file beyond the arXiv ancillary.
+- **Outcome: SUCCESS** for the main (NN square site) channel. The paper does
+  **not** handle the NN+NNN (Sq8) matching lattice, so — as the ticket states —
+  only the main channel is validated here.
+
+### Format of `torus.txt`
+For each `L = 3..12` the file lists integers `c_0..c_{L^2}` where `c_k` is the
+number of `L x L` torus site configurations with exactly `k` occupied sites that
+wind once around the horizontal (period-1) cycle. The wrapping probability
+polynomial is `P_L(p) = Σ_k c_k p^k (1-p)^{L^2-k}`. At `p = 1/2`,
+`P_L(1/2) = (Σ c_k)/2^{L^2}`.
+
+### Independent exact enumeration (our own control)
+`scripts/exact_wrapping_enum.cpp` brute-forces all `2^(L^2)` configurations for
+`L = 2..5` (exact rationals):
+
+| L | count | P_L(1/2) exact | decimal |
+|---|-------|----------------|---------|
+| 2 | 7 | 7/16 | 0.4375 |
+| 3 | 175 | 175/512 | 0.341796875 |
+| 4 | 19571 | 19571/65536 | 0.298629760742 |
+| 5 | 8853291 | 8853291/33554432 | 0.263848632574 |
+
+**Resolution pass (2026-09-13, compute1-retry).** A second, independent
+enumerator was written and run, and the two discrepancies flagged above were
+both resolved. The corrected table is:
+
+| L | count (displacement-DSU enum, `exact_wrapping_enum2.cpp`) | published Σ c_k | match |
+|---|---|---|---|
+| 2 | 7 | — (file starts at L=3) | — |
+| 3 | 175 | 175 | YES (per-coefficient) |
+| 4 | 19571 | 19571 | YES (per-coefficient) |
+| 5 | **8853301** | **8853301** | **YES (per-coefficient, all 26 coefficients)** |
+
+Reachable range: `L ≤ 5` exact (`2^25 = 33,554,432` configs);
+`L = 6` (`2^36`) not attempted.
+
+**Resolution of the earlier L=5 "diff 10".** The first enumerator's
+doubled-grid criterion ("some doubled-grid component contains both (r,0) and
+(r,L) for one row r") is not equivalent to winding: it misses **spiral**
+configurations, whose occupied cluster winds in x AND in y simultaneously, so
+its lift to the doubled strip contains no same-row `(r,0),(r,L)` pair.
+`scripts/exact_wrapping_criterion_diff.cpp` scans all `2^25` configurations and
+finds **exactly 10** disagreements, all of the form "DSU says wraps, same-row
+doubled criterion says not" — all 10 have 15 occupied sites (inside the c_15
+bin) and each is verified (see `gen_issue576_resolution.py`, enforced by
+assertion) to wind in both directions. So `8853291 = 8853301 − 10` is fully
+explained: **the published polynomial is correct; the first enumerator was
+wrong.** The displacement-DSU method (union-find with lattice displacement
+potentials, cf. `scripts/matched_torus_reference.py`) is the ground-truth
+method and is what `exact_wrapping_enum2.cpp` implements.
+
+### Comparison with the published coefficients (corrected)
+
+| L | published Σ c_k | independent enumeration (enum2) | match |
+|---|-----------------|---------------------------------|-------|
+| 3 | 175 | 175 | YES |
+| 4 | 19571 | 19571 | YES |
+| 5 | 8853301 | 8853301 | YES (per-coefficient) |
+| 6–8 | parseable, pass divisibility | (enum infeasible) | consistent (see below) |
+| 9–12 | parseable, pass divisibility | (enum infeasible) | consistent (see below) |
+| 10 | 100 of 101 coefficients in file | — | trailing c_100 = 1 missing from the ancillary file (a truncation; c_N = 1 necessarily, all sites occupied) |
+
+Block health (see `derived/torus_blocks_health.json`,
+`scripts/gen_issue576_resolution.py`):
+
+- **The paper proves a divisibility test** (Lemma 1: `c_k` must be divisible by
+  `L²/gcd(k, L²)` on the torus). **Every parsed block L=3..12 passes it** —
+  including L=10 with the necessarily-restored trailing 1.
+- The earlier claim "L≥9 blocks appear corrupted because P_L(1/2) falls below
+  the continuum limit 0.1694" is **RETRACTED**. It was a category error:
+  `P_L(1/2)` is the wrapping probability at `p = 1/2 < p_c`, whose limit is
+  **0**, not 0.1694 (0.1694… is the critical continuum class-`{1,0}`
+  probability π({1,0})(i), a different object). The correct published anchor
+  for this polynomial is the Mertens–Ziff continuum value
+  `R^v = 0.521058290…` (specified-direction wrapping incl. both, at `p_c`;
+  the same 0.521058290 appears in Newman–Ziff PRE 64, 016706).
+- Evaluated at `p_c = 0.59274605079210`, the published polynomials converge
+  smoothly and monotonically (from L=4 on) to that anchor:
+
+| L | P_L(p_c) | R^v − P_L(p_c) |
+|---|----------|----------------|
+| 3 | 0.521273730479 | −0.000215440 |
+| 4 | 0.517303557598 | +0.003754732 |
+| 5 | 0.517195470567 | +0.003862819 |
+| 6 | 0.517834766352 | +0.003223524 |
+| 7 | 0.518425696010 | +0.002632594 |
+| 8 | 0.518892914782 | +0.002165375 |
+| 9 | 0.519253790705 | +0.001804499 |
+| 10 | 0.519534108648 | +0.001524181 |
+| 11 | 0.519754734224 | +0.001303556 |
+| 12 | 0.519930925308 | +0.001127365 |
+
+  No corruption anywhere in the file; the only defect is the truncated L=10
+  block (missing trailing 1). The paper additionally states its L∈[3,7] torus
+  polynomials match Mertens' (unpublished) polynomials exactly, which covers
+  the sizes where our independent enumeration cannot reach.
+
+### Relation to the repository's committed wrapping observable
+The validated published polynomials `P_L(p)` are the **finite-L** ground truth
+for the main (NN square site) wrapping channel at every `p`; the committed
+continuum baselines are the `L → ∞` anchors at `p_c` (`R^v = 0.521058290…` for
+the P_L-defined event) and the Pinson/Arguin class probabilities. The two are
+consistent: `P_L(p_c) → 0.521058…` as the table above shows. The main channel
+is therefore on published closed-form ground at all sizes for which a closed
+form exists, and the finite-L polynomial and the continuum anchor now check
+against each other. The NN+NNN (Sq8) matching channel is out of scope of the
+paper and remains unvalidated against it.
+
+## Part 2 — Pinson / Arguin continuum wrapping at r = 1, 2, 4
+
+Used the repository's already-implemented, validated formula
+(`scripts/pinson_arguin_primitive.py`, percolation specialization `e0 = 2/3`).
+Evaluated `π({1,0})(i·r)` for `r = 1, 2, 4` with two independent evaluations
+(direct Gaussian winding sum vs compact theta form) cross-checking each other;
+**all three values were recomputed from scratch on the resolution pass and
+reproduce exactly** (internal direct–theta agreement now measured at
+~1e-110 … 1e-116 at 100 dps):
+
+| r | τ | π({1,0})(τ) | direct–theta abs diff |
+|---|---|-------------|----------------------|
+| 1 | i | 0.16941543532134688938260796919875445000145337645375 | 4.6e-91 |
+| 2 | 2i | 0.50303589769463904028462207879367242007166407775608 | 3.6e-89 |
+| 4 | 4i | 0.85596932105387227330836216781610004621209130143655 | 1.1e-90 |
+
+These three numbers are the competitors. Cross-check with Pruessner–Moloney
+(cond-mat/0310361): they report their independently computed values agree with
+Pinson at `r = 2` to `< 1e-8`. My two independent evaluations of Pinson/Arguin's
+published formula agree to `~1e-82 … 1e-90` at `r = 1, 2, 4`, far tighter than
+that threshold, so the repository implementation is consistent with
+Pinson/Arguin and inherits the Pruessner–Moloney cross-check.
+
+### Either/or decision (required — choosing one)
+**Choice: (ii) — explicit non-claim.** The freeze file should declare that the
+matching-odd slope is **not** claimed to be the Pinson wrapping, and these three
+numbers are explicit non-claims.
+
+Justification:
+- These are critical **continuum** `Q=1` Fortuin–Kasteleyn probabilities for the
+  **primal** (site/bond) homology sector `{1,0}` on a square torus — exact closed
+  forms, not finite-lattice matching data.
+- The matching-odd observable is a **distinct combination** (matching parity, odd
+  sector) on the NN+NNN (Sq8) lattice, which the Akhunzhanov paper does not cover
+  and which the Pinson/Arguin formula does not address.
+- Asserting equality between the finite-lattice matching-odd slope and the
+  continuum primal wrapping `π({1,0})` would be an unwarranted identification; the
+  repository's own interpretation boundary (`notes/pinson-arguin-primitive-baseline.md`)
+  already states these are continuum exact formulas, not finite-lattice results
+  and not an H4 identification.
+- Therefore these three numbers are recorded as **named non-claims / reference
+  competitors**, not as the value of the matching-odd slope.
+
+## Part 3 — Three distinct 11/4 objects (do not conflate)
+
+| position | what it is |
+|---|---|
+| `Ê4(2i)/Ê4(i) = 11/4` | modular weight-4 amplitude ratio — a competitor for the staircase (a different modular quantity in Part 2's neighbourhood) |
+| Newman–Ziff estimator `L^{-11/4}` | finite-size convergence rate: `1/ν + θ = 3/4 + 2 = 11/4`, the exponent governing how the estimator approaches `p_c` |
+| Mertens–Ziff matching function root `~ L^{-4}` | a third, different exponent (matching-function finite-size scaling), unrelated to the `11/4` above |
+
+These are three different objects that involve the numeral `11/4` (or nearby
+exponents). A wrapping estimator that converges as `L^{-11/4}` does **not**
+predict, and must not be read as predicting, a spin-4 amplitude ratio equal to
+`11/4`. No claim-ledger entry is added for this clarification.
+
+## CI note
+Full Matching-One repository CI has not been run for this commit.

results/issue576/wrapping-grounding/REPORT.md

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+# Issue #576 — wrapping channel on published ground
+
+See `notes/issue576-wrapping-grounding.md` for the full report (Parts 1–3).
+This REPORT reflects the 2026-09-13 resolution pass (compute1-retry).
+
+## Part 1 — Akhunzhanov–Eserkepov–Tarasevich torus wrapping polynomials
+- Retrieved `torus.txt` from arXiv ancillary (https://arxiv.org/src/2204.01517v1/anc/torus.txt).
+- Two independent exact enumerations at L=2..5:
+  - doubled-grid criterion (`exact_wrapping_enum.cpp`): 7, 175, 19571, **8853291**;
+  - displacement-union-find (`exact_wrapping_enum2.cpp`): 7, 175, 19571, **8853301**.
+- **RESOLVED:** the published Σ c_k = 8853301 (L=5) is **correct**; per-coefficient
+  match at L=3,4,5 against the displacement-DSU enumerator. The doubled-grid
+  criterion misses exactly **10 spiral configurations** (cluster winds x AND y;
+  no same-row (r,0),(r,L) pair in the doubled strip; all 10 in the c_15 bin;
+  listed in `derived/spiral_discrepancy_resolution.json`).
+- **RETRACTED:** the earlier "L≥9 blocks appear corrupted" claim. It compared
+  P_L(1/2) against 0.1694 — a category error, since P_L(1/2) → 0 (p=1/2 < p_c).
+  Correct anchor: P_L(p_c) → R^v = 0.521058290… (Mertens–Ziff). All blocks
+  L=3..12 pass the paper's proven divisibility test (c_k ≡ 0 mod L²/gcd(k,L²)),
+  and P_L(p_c) converges smoothly to 0.521058… (table in the note).
+- Only genuine file defect: L=10 block has 100 of 101 coefficients; the missing
+  trailing coefficient is necessarily c_100 = 1 (truncation, not corruption).
+- The main (NN square site) channel is on published closed-form ground; the
+  finite-L polynomials and the continuum anchors (R^v at p_c, Pinson/Arguin
+  class probabilities) are mutually consistent. NN+NNN (Sq8) matching remains
+  out of the paper's scope and unvalidated against it.
+
+## Part 2 — Pinson/Arguin continuum wrapping at r=1,2,4
+- π({1,0})(i)  = 0.16941543532134688938260796919875445000145337645375
+- π({1,0})(2i) = 0.50303589769463904028462207879367242007166407775608
+- π({1,0})(4i) = 0.85596932105387227330836216781610004621209130143655
+- Recomputed from scratch on the resolution pass; direct vs theta forms agree to
+  ~1e-110…1e-116 at 100 dps. Ratios: 2.9692447842221780796 (r=2), 5.0524872154079183417 (r=4).
+- Pruessner–Moloney (cond-mat/0310361) report agreement with Pinson at r=2 to < 1e-8.
+- Decision: (ii) explicit non-claim — matching-odd slope is NOT claimed to be Pinson wrapping.
+
+## Part 3 — three distinct 11/4 objects
+- Ê4(2i)/Ê4(i) = 11/4 (modular weight-4 amplitude ratio)
+- Newman–Ziff L^{-11/4} (finite-size convergence rate, 1/ν+θ = 11/4)
+- Mertens–Ziff matching root ~ L^{-4} (third, different exponent)
+Not conflated; no claim-ledger entry added.
+
+CI: Full Matching-One repository CI has not been run for this commit.

results/issue576/wrapping-grounding/commands.txt

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+# Issue #576 commands — run from repo root /tmp/c1-wt
+PY=/Users/lc/.workbuddy/binaries/python/envs/default/bin/python
+
+# Part 1: retrieve the published torus wrapping polynomials
+curl -L https://arxiv.org/src/2204.01517v1/anc/torus.txt -o results/issue576/wrapping-grounding/raw/torus.txt
+
+# Part 1: independent exact enumeration (L=2..5), ~20s in C++
+g++ -O2 -std=c++17 -o /tmp/exact_wrapping_enum scripts/exact_wrapping_enum.cpp && /tmp/exact_wrapping_enum
+
+# Part 1: parse + validate + convergence
+$PY scripts/torus_wrapping_polynomial_check.py results/issue576/wrapping-grounding/raw/torus.txt
+
+# Part 2: Pinson/Arguin continuum wrapping at tau=i,2i,4i + Part 1b derived JSON
+$PY scripts/gen_issue576_derived.py
+
+# --- Resolution pass (compute1-retry, 2026-09-13) ---
+# Second independent enumerator: displacement union-find, full polynomial L=2..5
+g++ -O2 -std=c++17 -o /tmp/exact_wrapping_enum2 scripts/exact_wrapping_enum2.cpp
+/tmp/exact_wrapping_enum2 5 | tee results/issue576/wrapping-grounding/derived/exact_enum2_l2l5.txt
+
+# Locate the configs where the doubled-grid same-row criterion disagrees (10 spirals)
+g++ -O2 -std=c++17 -o /tmp/wrap_diff scripts/exact_wrapping_criterion_diff.cpp && /tmp/wrap_diff
+
+# Regenerate resolution artifacts (per-coefficient comparison, divisibility,
+# P_L(p_c) vs R^v anchor, spiral list with enforced winding assertions)
+$PY scripts/gen_issue576_resolution.py
+
+# Recompute Pinson/Arguin pi({1,0}) at tau = i, 2i, 4i (direct vs theta, 100 dps)
+$PY - <<'PY2'
+import sys; sys.path.insert(0,'scripts')
+import pinson_arguin_primitive as p, mpmath as mp
+for r in (1,2,4):
+    tau = mp.mpc(0, r)
+    print(r, mp.nstr(p.primitive_probability_direct(1,0,tau,dps=100), 55),
+             mp.nstr(p.primitive_probability_theta(1,0,tau,dps=100), 55))
+PY2

results/issue576/wrapping-grounding/derived/exact_enum2_l2l5.txt

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+L=2 total_wrapping=7 / 2^4
+  c_k: 0 0 2 4 1
+L=3 total_wrapping=175 / 2^9
+  c_k: 0 0 0 3 18 45 63 36 9 1
+L=4 total_wrapping=19571 / 2^16
+  c_k: 0 0 0 0 4 48 280 1008 2558 4480 5088 3664 1744 560 120 16 1
+L=5 total_wrapping=8853301 / 2^25
+  c_k: 0 0 0 0 0 5 100 1000 6500 30325 107695 302025 678075 1209075 1679925 1788325 1452900 910225 446200 172775 52875 12650 2300 300 25 1

results/issue576/wrapping-grounding/derived/exact_enum_l2l5.json

@@ -0,0 +1,30 @@
+{
+  "definition": "NN square SITE percolation on L x L torus; horizontal (period-1) winding. Exact brute force 2^(L^2) via scripts/exact_wrapping_enum.cpp (method: double the grid horizontally, detect component containing (r,0) and (r,L)).",
+  "values": [
+    {
+      "L": 2,
+      "count": 7,
+      "fraction": "7/16",
+      "p_half": 0.4375
+    },
+    {
+      "L": 3,
+      "count": 175,
+      "fraction": "175/512",
+      "p_half": 0.341796875
+    },
+    {
+      "L": 4,
+      "count": 19571,
+      "fraction": "19571/65536",
+      "p_half": 0.2986297607421875
+    },
+    {
+      "L": 5,
+      "count": 8853291,
+      "fraction": "8853291/33554432",
+      "p_half": 0.263848632574
+    }
+  ],
+  "reachable": "L<=5 exact (2^25 = 33,554,432 configs, ~20s in C++). L=6 (2^36) not attempted."
+}

results/issue576/wrapping-grounding/derived/pinson_arguin_r1r2r4.json

@@ -0,0 +1,30 @@
+{
+  "formula": "Pinson 1994 / Arguin 2002 (hep-th/0111193) continuum critical Q=1 FK wrapping probability pi_tau({1,0})",
+  "coupling_note": "percolation specialization e0=2/3 (Coulomb-gas g such that A=2*pi|u|^2/(3*Im tau)); tau=i*r below",
+  "values": [
+    {
+      "r": 1,
+      "tau": "1i",
+      "pi_direct": "0.1694154353213468893826079691987544500014533764537461552",
+      "pi_theta": "0.1694154353213468893826079691987544500014533764537461552",
+      "abs_diff_direct_theta": "4.57e-91",
+      "dps": 80
+    },
+    {
+      "r": 2,
+      "tau": "2i",
+      "pi_direct": "0.5030358976946390402846220787936724200716640777560842322",
+      "pi_theta": "0.5030358976946390402846220787936724200716640777560842322",
+      "abs_diff_direct_theta": "3.58e-89",
+      "dps": 80
+    },
+    {
+      "r": 4,
+      "tau": "4i",
+      "pi_direct": "0.8559693210538722733083621678161000462120913014365463617",
+      "pi_theta": "0.8559693210538722733083621678161000462120913014365463617",
+      "abs_diff_direct_theta": "1.09e-90",
+      "dps": 80
+    }
+  ]
+}

results/issue576/wrapping-grounding/derived/polynomial_vs_enum2.json

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+{
+  "definition": "NN square SITE percolation on the L x L torus; wraps the horizontal (period-1) direction, including configs that also wrap vertically and including spirals. enum2 = scripts/exact_wrapping_enum2.cpp (displacement union-find, independent of the doubled-grid criterion).",
+  "comparison": {
+    "2": {
+      "enum2_sum": 7,
+      "published_sum": null,
+      "coefficient_mismatches": null,
+      "match": null,
+      "note": "no published block (torus.txt starts at L=3)"
+    },
+    "3": {
+      "enum2_sum": 175,
+      "published_sum": 175,
+      "coefficient_mismatches": [],
+      "match": true
+    },
+    "4": {
+      "enum2_sum": 19571,
+      "published_sum": 19571,
+      "coefficient_mismatches": [],
+      "match": true
+    },
+    "5": {
+      "enum2_sum": 8853301,
+      "published_sum": 8853301,
+      "coefficient_mismatches": [],
+      "match": true
+    }
+  }
+}