Lit retrieval: cylinder/TM literature vs width-4 all-p matching identity (#711, do not merge)

[LightChainr]

Draft. Do not merge. Retrieval only, closes nothing, parent #650, ticket #711. Independent of #708/#710 (no code, no census, no transfer engine, no Huawei). Additive on main@eb89e94. No docs/STATUS.md edit.

Deliverable: notes/lit-cylinder-tm-width4-20260912.md — independent literature retrieval on what of the width-4 all-p matching identity structure is already published, and under which names.

Source marking

Source	Mark
Jacobsen 2015, J. Phys. A 48 454003, arXiv:1507.03027 (arXiv HTML v1 + PDF v1)	PRIMARY_TEXT_READ
Scullard & Jacobsen 2012, J. Phys. A 45 494004, arXiv:1209.1451 (PDF)	PRIMARY_TEXT_READ
Jacobsen & Scullard 2013, J. Phys. A 46 075001	ABSTRACT_ONLY
Scullard & Jacobsen 2015, arXiv:1511.04374 (ar5iv HTML + PDF)	PRIMARY_TEXT_READ
Mertens & Ziff 2016, PRE 94 062152, arXiv:1603.07289 (ar5iv HTML + PDF)	PRIMARY_TEXT_READ
Akhunzhanov, Eserkepov & Tarasevich 2022, J. Phys. A 55 204004, arXiv:2204.01517	PRIMARY_TEXT_READ
Yang & Zhou 2024 Comment, J. Phys. A 57 258001	ABSTRACT_ONLY
Jacobsen 2024 Reply, J. Phys. A 57 258002	ABSTRACT_ONLY (IOP body bot-blocked; not on arXiv)

Tripwire met: ≥3 fetched primary papers plus Jacobsen 2015 Table 2 / Eqs. (13),(50) with quotations. Every quotation copied from fetched text; none reconstructed.

Answers (compact)

1. Jacobsen 2015, square-site cylinder n=4: proves the eigenvalue identity P_B=0 ⇔ Λ_open=Λ_closed (Eq. (13), finite n, m→∞) via an intermediate-value argument, plus the numerical Table 2 datum 0.5914171708531384817988341017359231779642. The graph polynomial is a finite-basis difference of event weights P_B = Z_2D − q Z_0D (Eq. (4)) — not phrased as wrapping probabilities, not a finite-m trace identity. p_c(n) − p_c = O(n^{-4}) (Eq. (50)) is observed, and the paper says so. ArXiv-HTML vs PDF equation-numbering discrepancy recorded in the note (HTML (50) = PDF (44)).
2. Scullard–Jacobsen 2012–2014: the difference P_2D − q P_0D is the definition at finite basis (SJ12 Eq. (5), "eq. (5) is the main result of this paper"; SJ15/S1 Eq. (2)), not only a limit or root statement. Root-as-p_c interpretation is the infinite-B limit; contraction–deletion equivalence left open in SJ12. Not our object: the channels are 2D/0D event weights, not P_2/P_0 matching channels and not traces.
3. Finite-length displacement p_{n,m} − q_n ~ c ρ^m/m: negative retrieval result — not found for percolation wrapping/matching. In print: "convergence being exponential in m" (S1 §4.3, no rate) and power-law FSS p*_L − p_c ~ L^{−w}, w ≈ 4 vs L^{−2.75} (Mertens–Ziff Eq. (20) et seq.); Akhunzhanov et al. use Σ_k A_k L^{−Δ_k} (Eq. (9)). The ρ^m/m machinery is applied in the literature to Ising free energy only.
4. Block decompositions at n=4: S1's string-graded T~ = ⊕ T^{(s=2k)} ⊕ T_open ⊕ T_closed (Eq. (9)) is in print — six sectors at n=4, 35 reduced states each for the two s=0 sectors — not 5+15+16. Mertens–Ziff's M_L(p) (Eq. (20)) is a matching function as a difference of two wrapping-probability sectors at finite L. No tr B_15^m − tr B_5^m anywhere.
5. Jacobsen 2024 Reply (57 258002): ABSTRACT_ONLY; published one-sentence abstract via Crossref (quoted verbatim in the note). Body unreachable (IOP bot page, no arXiv record). Subject is the Yang–Zhou helical-h(n) / extrapolation-digits dispute — no Q3-type displacement formula.

Explicitly not in print (checked, negative)

• B_5, B_15, B_16, or tr B_15^m − tr B_5^m — no appearance; the note nowhere attributes them to a published paper.
• No 5+15+16 sector split; no "difference of two traces" identity.
• No c ρ^m/m displacement for a percolation cylinder estimator.

Do not merge. Do not close #711 from here.

[LightChainr]

Independent Grok check (not the glm log). Jacobsen 2015 HTML: (4) P_B=Z_2D-q Z_0D; (9) string-graded T~; (13) P_B=0⇔Λ_open=Λ_closed for finite n, m→∞; (50) O(n^{-4}) is observed, not deduced from (49); Table 2 n=4 matches q4. Mertens–Ziff (20) is a wrapping-probability difference on the matching lattice, not a trace identity and not our digital-Alexander M. No 5+15+16 and no tr B_15^m-tr B_5^m in these sources. No published c ρ^m/m for percolation cylinder estimators found here (negative retrieval, not a no-go). Jacobsen 2024 Reply remains ABSTRACT_ONLY.

Keep for #710: the all-p finite-m trace formula is not a restatement of Jacobsen (13). Keep for #705/#718: polynomial-level M=0 vs wrapping criterion is MZ; eigenvalue crossing is limits-first.

Do not merge. Do not close #711. #712/#714 still running.