From 925e98bd825eb73588cf0fa3f111cf146695488a Mon Sep 17 00:00:00 2001 From: Light Chain Date: Wed, 9 Sep 2026 23:59:54 +0800 Subject: [PATCH] Add venue-retrieval notes for P4 matching-odd scalar closure (#696) Retrieval-only literature note per issue #696: wrapping/crossing primary sources (Langlands-Pouliot-Saint-Aubin 1994, Pinson 1994, Newman-Ziff 2001, Mertens-Ziff 2016, Pruessner-Moloney 2004, Simmons-Kleban-Ziff 2007) read from fetched full texts where available, with lattice sizes, venues, and PRIMARY_TEXT_READ / ABSTRACT_ONLY / [LIT] markers. Independent venue fit assessment and stress-test of the prior Grok assessment. No Monte Carlo, no p_c claim, no STATUS/ROADMAP edits, P4 draft not merged. --- notes/venue-retrieval-p4-20260909.md | 314 +++++++++++++++++++++++++++ 1 file changed, 314 insertions(+) create mode 100644 notes/venue-retrieval-p4-20260909.md diff --git a/notes/venue-retrieval-p4-20260909.md b/notes/venue-retrieval-p4-20260909.md new file mode 100644 index 00000000..668bb278 --- /dev/null +++ b/notes/venue-retrieval-p4-20260909.md @@ -0,0 +1,314 @@ +# Venue retrieval for P4 (matching-odd scalar closure) — wrapping/crossing literature + +Ticket: [#696](https://github.com/LightChainr/Matching-One/issues/696). Retrieval and notes only. +The P4 draft read for this note is `docs/manuscripts/p4-matching-odd-scalar-closure/README.md` +on branch `pr688` (= `pull/688/head`), unmerged, read with `git show pr688:...`. +No P4 result was recomputed, no Monte Carlo was run, no `p_c` claim is made, and +P3's projective statistic is not imported. `docs/STATUS.md` and `docs/ROADMAP.md` untouched. + +Literature marking follows the repo convention (p2 README / p3 manuscript): +`PRIMARY_TEXT_READ` = the full text was fetched and read in this session; +`ABSTRACT_ONLY` = bibliographic record plus (part of) the abstract only; +`[LIT]` = known citation, not fetched. + +## 0. What was actually fetched + +| # | paper | venue | how read | marker | +|---|---|---|---|---| +| S1 | Langlands, Pouliot, Saint-Aubin, *Conformal invariance in two-dimensional percolation* | Bull. Amer. Math. Soc. **30**(1), 1–61 (1994); arXiv:math/9401222 | full text (arXiv PDF, 60 pp.) | PRIMARY_TEXT_READ | +| S2 | H. T. Pinson, *Critical percolation on the torus* | J. Stat. Phys. **75**, 1167–1177 (1994), DOI 10.1007/BF02186762 | bibliographic record + opening abstract sentence; Springer/ADS full text bot-blocked | ABSTRACT_ONLY | +| S3 | M. E. J. Newman, R. M. Ziff, *Fast Monte Carlo algorithm for site or bond percolation* | Phys. Rev. E **64**, 016706 (2001); arXiv:cond-mat/0101295 | full text (APS harvest PDF, 16 pp.) | PRIMARY_TEXT_READ | +| S4 | S. Mertens, R. M. Ziff, *Percolation in finite matching lattices* | Phys. Rev. E **94**, 062152 (2016); arXiv:1603.07289 | full text (ar5iv HTML) | PRIMARY_TEXT_READ | +| S5 | G. Pruessner, N. R. Moloney, *Winding clusters in percolation on the torus and the Möbius strip* | J. Stat. Phys. **115**, 839–853 (2004); arXiv:cond-mat/0310361 | full text (ar5iv HTML) | PRIMARY_TEXT_READ | +| S6 | J. J. H. Simmons, P. Kleban, R. M. Ziff, *Percolation crossing formulae and conformal field theory* | J. Phys. A **40**, F771–F784 (2007); arXiv:0705.1933 | full text (ar5iv HTML) | PRIMARY_TEXT_READ | +| S7 | J. Cardy, *Critical percolation in finite geometries* | J. Phys. A **25**, L201 (1992) | citation only | [LIT] | +| S8 | G. M. T. Watts, *A crossing probability for critical percolation in two dimensions* | J. Phys. A **29**, L363–L368 (1996), DOI 10.1088/0305-4470/29/14/002 (Crossref) | citation only | [LIT] | +| S9 | R. K. Akhunzhanov, A. V. Eserkepov, Yu. Yu. Tarasevich, *Exact percolation probabilities for a square lattice: site percolation on a plane, cylinder, and torus* | J. Phys. A **55** (2022); arXiv:2204.01517 | abstract + bibliographic record | ABSTRACT_ONLY | + +All quotes below were taken from the fetched texts of S1, S3–S6 (or, for S2, from +the abstract fragment visible on the Springer/ADS record). + +## Q1. Has a matching-odd / orientation-odd wrapping contrast been published? + +**Answer: not as a cos 4θ orientation contrast of a matching function, in anything I +could read. The two halves of the observable each have a published home; their +oriented difference does not.** Caveat marked below. + +The published "odd" objects I found are odd in **p**, not in orientation: + +- Mertens–Ziff (S4) define the matching function on the torus and prove the exact + wrapping identity (their Eq. 20, quoted verbatim): + + > "M_L(p) = R^x_L(p) − R̂^x_L(1−p), x ∈ {c, b, e, h} (20) … **This is the main + > result of this paper.**" + + This is the published ancestor of P4's matching/primal pairing `S = (R_G + R̂)/2`, + `D = (R_G − R̂)/2`, and of the finite Russo identity the P4 draft uses as a spine + (MZ derive `N_L(p) − N̂_L(1−p) = L²χ(p) + O(1)` from it). It is odd under + `p → 1−p` combined with lattice duality — it says nothing about lattice + orientation θ. +- Newman–Ziff (S3) define the four torus wrapping probabilities `R^(h), R^(v), R^(b), R^(e)` + and the channel difference (their Eqs. 11–12): + + > "R^(1) = R^(h) − R^(b) = R^(e) − R^(h) = ½(R^(e) − R^(b)), (12)" + + a difference of wrapping channels on the **same** lattice — the closest published + thing to P4's "first-minus-second pairing" logic, but the difference is over + topological channel, not over orientation, and it is not matching-odd. + +Orientation enters the published torus literature in two other ways, neither of +which is a spin-4 contrast of the matching function: + +- **Per homology class, not harmonic.** Langlands–Pouliot–Saint-Aubin (S1, §3.7) + ask, in their words: + + > "We can ask for the probability, always at criticality, that a given subgroup Z + > of H1(S) is contained in the image, and expect that the response depends only on + > the conformal class of S." + + and simulate the square torus `S1 = C/(Z + ZiZ)` at mesh 1/500 plus a branched + double cover, reporting `π̂(1,0), π̂(0,1), π̂(1,1), π̂(1,−1), π̂(0), π̂(H)` + (their Table 3.7). Diagonal classes (1,±1) are measured, i.e. 45°-oriented + wrapping exists as data — but no first-vs-second orientation pairing is formed + and no cos 4θ coefficient is extracted. Their Table 3.7 values for the two + isomorphic tori (e.g. `π̂(1,0)` 0.1693 vs 0.1700) are presented as a + conformal-invariance check, with differences at the level of their statistical + error. +- **Aspect-ratio (modulus) dependence, not orientation harmonic.** Pinson (S2, + ABSTRACT_ONLY) computes "the various crossing probabilities defined by + R. Langlands, P. Pouliot, and Y. Saint-Aubin" on the torus with CFT; her + winding-cluster formulas were tested numerically by Pruessner–Moloney (S5), + who confirm the topological prediction `𝒫̂(X, r) = 𝒫̂(0, r)` ("This is in + perfect agreement with our numerical results") and check winding numbers + `(1,0), (1,±1), (1,±2), (1,±3)` across 14 aspect ratios 30/30 … 900/1. Again: + an aspect-ratio (modulus) axis, no orientation-odd contrast. + +A targeted search for a `cos 4θ` / four-fold harmonic of a percolation wrapping +observable returned nothing (closest hits were exact wrapping-polynomial +enumerations, S9, which are again orientation-unresolved). + +**Caveat to keep:** S2 (Pinson 1994) could not be read in the primary; her paper is +the one published text where a harmonic decomposition of torus crossing data could +still be hiding. The P4 bib pass (P4 README §10 item 2) must read Pinson 1994 in the +primary before the paper claims channel novelty. Until then the correct statement is: +**new among the texts read here, with S2 unverified.** + +Bonus cross-check (supports P4's channel semantics): P4's exact map +`DeltaS_cross = −DeltaS_either` (even) and `D_either = D_cross` (odd) is the +discrete counterpart of identities already in the published record — +MZ Eq. (19) `R^1_L(p) = R̂^1_L(1−p)` and NZ Eq. (11) `R^(e) = 2R^(h) − R^(b)`. +The P4 erratum (#108) reclassification is consistent with these; nothing in the +fetched texts contradicts the draft's channel algebra. + +## Q2. Finite-size scalar closure: what published papers test, and what they do when it fails + +Three of the read texts are genuine analogues for "signal exists; one scalar does +not close it": + +1. **Mertens–Ziff 2016 (S4)** is the closest structural analogue, and it *succeeds* + with one scalar + corrections. The scaling-limit odd matching function collapses: + + > "M_L(p) = f(z) − f(−z) (36) in the scaling limit. A scaling plot of M_L(p) is + > shown in the inset of Fig. 5. This curve is universal for systems of this shape + > (square torus), except for a scale factor on z." + + But the pre-asymptotic data require **two extra correction exponents** fitted + beyond the known `1/ν = 3/4` (their Eq. 38 analysis): "These plots give + 2−x = −3.42 and 2−y = 0.705", and their summary of the residuals is worth + quoting at the P4 draft directly: + + > "Finite-size effects explain why many of our observations and analyses agree + > only approximately." + + This is the published version of "the amplitude-like mode closes, the shape mode + does not": MZ need a two-exponent correction tower to make their scalar story + consistent, and they say so in exactly the register P4 uses for its §6 failures. +2. **Pruessner–Moloney 2004 (S5)** is a *published scalar-closure failure that stayed + a failure* — the honest precedent for P4 §6.3. Testing Pinson's CFT amplitudes + for multiple winding clusters: + + > "one might be tempted to find a systematic dependence of C((1,0),n) and + > α((1,0),n) on n, such as an exponential and a second order polynomial, + > respectively. However, we were unable to identify these functions." + + and, critically for P4's methodology, their error budget statement: + + > "the main source of error is not statistical, but systematic, namely in the + > choice of the specific function" + + A frozen-prediction paper can cite this line verbatim: at 10⁶–10⁹ samples the + residual is the model, not the noise — which is precisely P4's situation at + 500M replicas. +3. **Newman–Ziff 2001 (S3)** shows the standard fallback when a single clean law is + not available: use a statistic whose limit is known without a fit. Their + threshold estimator is the maximum of the channel-difference `R^(1)`, and in 3D + they fit only after the fact: "we can estimate p_c by varying the scaling + exponent until an approximately straight line is produced." Published practice + tolerates this; P4's frozen-prediction discipline is *stricter* than what NZ did + in the same journal. + +**Refinement of the ticket's question:** none of the read texts treats a scalar +failure as evidence for a non-scalar (Jordan-type) mechanism — MZ absorb it into +correction exponents, P–M leave it unidentified, NZ avoid it by statistic choice. +P4's low-rank mixing claim is therefore *stronger* than anything published in this +niche, and the paper should present the rank-2/Jordan ordering (its §7) as a +hypothesis ranking diagnostic, not as an identification — the draft already does +this (its §6.2 "compatible, not identified" clause). The MZ corrections tower +(`L^(−x)`, `L^(−y)` with x ≈ 5.42 unknown) is the conservative alternative +explanation a PRE referee will reach for first, and the draft's §7 evidence +(one projected derivative channel closing at −0.009σ while its companion misses at ++2.70σ) is exactly the observation that distinguishes the two. That contrast should +be made explicit in the manuscript; it currently lives only in P50 REPORT.md prose. + +## Q3. Lattice sizes in the published wrapping/crossing FSS record + +Actual linear sizes from the fetched texts: + +| paper | engine | linear sizes | samples | +|---|---|---|---| +| NZ 2001 (S3) | MC (Newman–Ziff algorithm) | 128×128 (pc estimate), **1024×1024** (stretched-exponential), 512×512 (Fig. 10 context) | "more than 7.3×10⁹ separate samples, about half of which were for systems of size 128×128" | +| MZ 2016 (S4) | exact enumeration + MC | exact **L = 3–11**; MC "L = 16, 24, 32, 48", "up to L = 128" | exact, plus standard MC runs | +| LPS 1994 (S1) | MC at criticality | square torus mesh 1/**500** (500×500); branched cover square side **282**; rectangles/parallelograms to 1000×1000 (Table 3.2) | "The sample size for all our experiments was at least 10⁵, and very often" more (10⁶) | +| P–M 2004 (S5) | MC, patch-parallel | patches L = 10, 100, 1000; total lattices **300² to 30000²** (9×10⁸ sites) | "at least 10⁶ realizations"; "of the order of 10⁹ samples" for r=1 | +| SKZ 2007 (S6) | hull-walk MC | **512×512 bonds** primary; FSS at L = 64, 128, 256, 1024 | "we were able to generate 3.3×10¹¹ hulls on a lattice of 512×512 bonds" | + +So the published MC record for wrapping observables sits at **L ≈ 512–1024 for the +headline finite-size statements**, with one paper (P–M) pushing to 3×10⁴, and the +exact-enumeration branch deliberately working at L ≤ 128 where exactness or frozen +predictions substitute for size. + +P4's N = 145–425 sites with 500M replicas per point is therefore: + +- **above** the exact-enumeration branch (MZ: L = 3–11 exact; Akhunzhanov et al. S9 + exact wrapping polynomials at small L, ABSTRACT_ONLY) where small L is + compensated by exactness; +- **below** the MC branch's comfort zone. 500M replicas is comparable to NZ's + 7.3×10⁹ samples and P–M's 10⁹, so the *statistical* budget is normal for this + literature; what is not normal is spending it entirely below L ≈ 512. + +**Verdict on the ticket's question ("normal computational paper, or will referees +demand L ~ 10³–10⁴?"):** referees will demand *more L*, specifically at least one +lineage at L ≥ 512, because every MC FSS claim in the table above that a referee +would recognize made it at 512+. They will not demand 10⁴ — that was needed only +for P–M's winding-number tail probabilities (~10⁻⁹), not for amplitude/shape +tests. P4's own §8 item 8 ("a second independent doubling curve (new geometry, not +a rerun) is the natural referee ask") is correct, and the literature adds a second +axis: the new geometry should also be **larger**, not just different. + +## Q4. Venue fit, independently + +- **Physical Review E — fit.** Scope: statistical, multiphase, and soft-matter + physics, including computational statistical mechanics. The entire + wrapping-probability MC literature this paper would cite lives here: NZ (PRE 64, + 016706) and MZ (PRE 94, 062152). A methods-plus-percolation paper with frozen + predictions and a negative scalar-closure result is a natural PRE + Statistical Physics article. Analogue: **Mertens–Ziff 2016** — same journal, + same observables, likewise without a new exponent claim at its core. +- **JSTAT / J. Stat. Phys. — fit.** Scope: statistical physics theory and + computation (JSTAT), and the older JSP carries exactly the torus lineage: Pinson + (JSP 75) and Pruessner–Moloney (JSP 115). Analogue: **Pruessner–Moloney 2004** — + torus winding observables, CFT-null testing, honest systematic-error statement. + If the paper leans on the CFT/Pinson connection, JSTAT/JSP is arguably the more + topical home; if it leans on the frozen-prediction methodology, PRE. +- **J. Phys. A — fit (narrower).** Scope: mathematical and theoretical physics, + including statistical mechanics and its computational study. Precedent: SKZ + crossing formulae (J. Phys. A **40**, F771, Fast-Track) and Watts (J. Phys. A + **29**, L363). Best if the final paper foregrounds the exact channel algebra and + the conformal-candidate reading (`x = 21/4`, STATUS line 68 level only); + weaker if the paper's center of mass is the frozen-prediction governance. +- **Physical Review Letters — stretch (recommend against on current evidence).** + The ticket's tripwire applies: I fetched no PRL percolation analogue that + carries a finite-size signal with no new exponent, no operator identification, + and no `p_c`. The PRL-adjacent percolation results in the fetched set all had a + sharp universal number at stake (NZ's stretched-exponential exponent 4/3 vs + Gaussian; SKZ's exact crossing densities at 3.3×10¹¹ hulls). P4's headline is a + rejection + three falsifications on N ≤ 425 — the PRL editors' "beginning a new + line of important follow-up work" bar is not met by a paper whose own §8 lists a + mandatory second lineage as missing. **Do not recommend PRL.** +- **SciPost Physics — plausible secondary, not first choice.** Scope: core + scientific physics with open peer review; percolation FSS papers appear there. + The open-review format would actually suit P4's heavy artifact-citation style + (referees can check JSON fields). But it adds no reach beyond PRE, and the + frozen-prediction governance story will read as unusual to a general + statistical-physics readership. Agree with the prior assessment that it is not + the home. + +**Summary:** PRE first, JSTAT/JSP second, J. Phys. A if the exact-algebra angle +grows, PRL no, SciPost acceptable fallback. This independently agrees with the +prior assessment's point 1. + +## Q5. Readiness: is the second independent doubling curve actually required? + +What published practice shows: + +- **MZ 2016** published with a single lattice family (square torus) — but with + exact data L = 3–11 *plus* MC to L = 128, i.e. size coverage, not just replica + coverage. +- **P–M 2004** ran the same analysis for site *and* bond percolation as an + internal cross-check, and across 14 aspect ratios; their published confidence + rests on that breadth. +- **LPS 1994** checked the same torus probability against an isomorphic branched + cover — a deliberate second realization of the same conformal class (their + Table 3.7, S1 vs S2 columns). +- **NZ 2001** validated the algorithm across site/bond, several lattices, and 2D/3D. + +So the discipline in this niche is: a single-lineage claim passes only when +something else is exact or independently varied. P4 has 500M-replica precision and +frozen predictions (its equivalent of MZ's exactness), but Block III — where two of +the three scalar failures live — is one lineage (N = 65→130, 85→170 trained; +145→290 held out), and the draft says so (§8.8). + +**Verdict:** a clearly labelled single-lineage limitation *can* pass at PRE (MZ's +"agree only approximately" is precedent for publishing with acknowledged +finite-size systematics), but the referee will ask for the second doubling curve +and the paper is stronger pre-empting that with one new geometry at N ≥ 512 (which +is simultaneously the Q3 answer). The draft's §10 item on this is correctly +listed as referee-ask, not as optional polish. Also worth keeping from Q2: the +paper should surface the MZ-style correction-exponent alternative explanation and +show where its data discriminate against it — that pre-empts the most likely +theory-side referee objection and costs no new computation (it is analysis of +committed artifacts). + +## Stress-test of the prior Grok assessment (agree / disagree / refine) + +1. **"PRE or JSTAT after a real writing pass; not PRL / SciPost main."** — **AGREE.** + Independently derived above from fetched analogues (MZ → PRE; P–M/Pinson → + JSP/JSTAT; SKZ/Watts → J. Phys. A as the theory-leaning alternative). The PRL + tripwire was checked and holds: no fetched PRL analogue lacks a new + exponent/`p_c`. +2. **"Most 'new physical fact' of the four objects *if* the signal survives larger N."** + — **AGREE, with a refinement.** "Larger N" in this literature means L ≥ 512 + (every MC headline result in the table above was made at 512+), which is a + different simulation regime from N ≤ 425. If the signal does *not* survive, the + salvageable paper is the methodology-plus-falsification structure (P–M 2004 is + precedent that an honest "we could not identify the scalar law" paper is + publishable), not the signal claim. +3. **"N ~ 10² is the obvious referee objection; 500M replicas do not buy systematic + finite-size control."** — **AGREE, and it can now be sharpened with numbers:** + 500M replicas is normal for this literature (NZ 7.3×10⁹ samples; P–M ~10⁹); + the linear-size deficit (425 vs 512–1024) is the objection, and the + correction-exponent alternative (MZ's `2−x = −3.42`, `2−y = 0.705` tower) is + the form the objection will take. Referees will not require 10⁴ sites — that + demand belongs to tail-probability studies (P–M's ~10⁻⁹ winding probabilities). +4. **"Mechanism claim must stop at low-rank non-scalar mixing; no LCFT module."** + — **AGREE.** Nothing in the fetched texts supports an operator identification; + the closest published treatments (MZ's correction exponents; P–M's refusal to + identify `C(n)`, `α(n)`) both stop before any operator claim. P4's draft §7 + already stops exactly there; keep it. +5. **"Do not use the N=580 aspect ladder as physics evidence."** — **AGREE.** The + draft's own §8.2 records the ladder verdict (`underpowered`) and keeps it a + limitation; nothing in this retrieval touches that. + +Net: five agreements, two refinements (the L ≥ 512 number; the correction-exponent +alternative explanation that should be named and tested in the manuscript's +analysis, not just anticipated). + +## Claim boundary restated + +- No `p_c` inference anywhere above. No STATUS/ROADMAP promotion. +- All numbers quoted from fetched literature are identified by paper and, where + relevant, by equation/table; nothing was recomputed from P4 artifacts. +- P3's projective statistic appears nowhere above as a P4 result. +- S2 (Pinson 1994) is the one unresolved primary; it is flagged rather than guessed + at. If the P4 bib pass cannot obtain the text, the channel-novelty claim must be + softened to "new among surveyed primary sources."