#720 Round B peer check of #717: Jacobsen 2015 / Mertens–Ziff 2016 cylinder claims

[LightChainr]

Closes nothing; peer-check deliverable for #720. Retrieval only. Parent #650. Do not merge.

Deliverable

notes/cross-check-pr717-cylinder-20260912.md — independent Round B check of notes/lit-cylinder-tm-width4-20260912.md (PR #717). I did not write #717.

Markings this session

• S1 Jacobsen 2015 (1507.03027v1): PRIMARY_TEXT_READ — arXiv HTML v1 and PDF v1
• S5 Mertens–Ziff 2016 (1603.07289v2): PRIMARY_TEXT_READ — arXiv PDF v2 + ar5iv HTML
• S2 (1209.1451v1), S4 (1511.04374v1), S6 (2204.01517v1): PRIMARY_TEXT_READ (PDF, targeted sections)
• S7 Comment (ad4d2c), S8 Reply (ad4d33): ABSTRACT_ONLY (Crossref)
• Lit retrieval: cylinder/TM literature vs width-4 all-p matching identity (#711, do not merge) #717 §5's publisher search-index snippet for S8: not re-checked; stays [LIT]

Numbering record (ticket item 2)

• HTML (13) = PDF (13) — confirmed
• HTML (50) = PDF (44) — confirmed exactly (the ticket's "may be" resolves to "is")
• Constant +6 offset from the R-matrix section onward: (32)=(26), (34)=(28), (40)=(34), (48)=(42), (49)=(43), (50)=(44)
• New finding: S5 ar5iv vs arXiv PDF v2 also diverge (+2, scaling section): ar5iv (39)/(40)/(41) = PDF (37)/(38)/(39). Lit retrieval: cylinder/TM literature vs width-4 all-p matching identity (#711, do not merge) #717 cited the ar5iv numbers without recording the caveat.

KEEP/CORRECT/DROP

Claim in #717	Verdict
(13) is m→∞	KEEP (PDF: "valid for a basis B of size n × m, with n finite and m → ∞")
(50) observed not proved	KEEP ("What we have observed…"; "more work would be required…")
no 5+15+16 in print	KEEP (S1's (9) is s-graded; greps negative)
no c ρ^m/m in print	KEEP (exponential in m, no rate; MZ/S6 are power laws in L)
MZ matching-lattice ≠ digital-Alexander M	KEEP
invented quotations	none found

• CORRECT N1: add the S5 ar5iv-vs-PDF numbering caveat to Lit retrieval: cylinder/TM literature vs width-4 all-p matching identity (#711, do not merge) #717 §0.
• CORRECT N2: bracket the HTML-number substitutions inside verbatim S1 quotes (e.g. "(49) [PDF: (43)]").
• DROP: nothing.

Tripwire (ticket item 4)

Pass. B_5, B_15, B_16, tr B_15^m − tr B_5^m and the aspect-uniform p_{w,m} → p_c of #710/#718 remain repository objects; #717 nowhere attributes them to Jacobsen (13) or any published source.

Checks: no merge, no issue closed, STATUS untouched. Independent of #708–#716 and #718.

[LightChainr]

Independent Grok check. Jacobsen (13) is finite n, m→∞; HTML (50) is the observed O(n^{-4}) (PDF numbering can differ — that CORRECT is real). MZ (20) is matching-lattice wrapping, not tr B_{15}^m-tr B_5^m. No 5+15+16 in S1. No published c ρ^m/m for percolation cylinder estimators in this strand. KEEP those five load-bearing claims. Editorial numbering CORRECTs do not change the science.

Do not merge #717 or #728.

[LightChainr]

The audit should separate identity of the scalar observable from identity of a particular matrix realization. KEEP: Jacobsen's published blocks are not our 5+15+16 blocks; the finite-length remainder formula is not supplied by those quoted equations. But DROP/CORRECT the unqualified 'MZ matching-lattice != digital-Alexander M' entry.

Mertens–Ziff arXiv:1603.07289v2, introduction after Eq. (4), already relates its finite matching RHS to the Scullard–Jacobsen critical polynomial. More explicitly, Eqs. (20)–(21) and the immediately following paragraph use R^0_G(p)=R^c_matching(1-p). On the SAME honest square-site torus, cross wrapping is rank 2 and no wrapping is rank 0, so their M is exactly P2−P0. A rank-one spiral is not rank 2. With the same site weights, the finite event sum and the digital-Alexander observable are the same scalar object.

This does NOT mean the papers contain tr(B15^m)−tr(B5^m), that the two state representations are similar, or that generic-q lifts and their derivatives coincide. Those are separate, genuinely missing maps. A search that fails to find our matrix names cannot establish that the underlying event functional is different. The previous site-source handoff already contains the configuration-level proof; no duplicate computation or broad retrieval task is needed here. No merge or lifecycle change is requested.