[Round B peer check] Cross-check of #724: thermal m λ^m vs Jordan/LCFT diagnostics (#727)

[LightChainr]

Closes #727 on merge (deliverable only — review/merge decisions belong to the owner). Ticket: #727 (parent #650). Peer check of PR #724; #714 is the checked note.

Draft. Do not merge. No docs/STATUS.md entry. Does not adjudicate #275 and does not declare it solved.

Deliverable

notes/cross-check-pr724-jordan-20260912.md

What was done

• Full read of the [Grok retrieval] Thermal m λ^m vs Jordan/LCFT diagnostics — literature note (#714) #724 note (git show pr724:notes/lit-thermal-jet-jordan-20260912.md, commit ef6bdcf).
• Mandated re-fetches (2026-09-12, ar5iv):
  • Vasseur–Jacobsen–Saleur arXiv:1206.2312 — eq. (11) and the "rank-2 Jordan cell mixing the two fields ψ̃_ab and ε" statement; conclusion paragraph distinguishing correlator logs from Boltzmann-weight-derivative logs; eqs. (8)/(9). All match [Grok retrieval] Thermal m λ^m vs Jordan/LCFT diagnostics — literature note (#714) #724 verbatim.
  • Gurarie 1993 (hep-th/9303160) — L0 Jordan cell eqs. (13)/(19), two-point functions eq. (22), pseudo-operator sentence, same-dimension fusion criterion. Matches.
• Spot-checks beyond the mandate: Cardy 1999 (all three quotes verbatim; footnote [17] caveat added), Bamieh 2002.05001 (semisimple hypothesis verbatim; confirmed the word "Jordan" never appears).

KEEP / CORRECT / DROP

Verdict	Count	Items
KEEP	13	VJS (8)/(9)/(11) + conclusion paragraph; Gurarie Jordan cell + (22); Cardy unitarity + q-derivative passages; core distinction (m λ^{m-1} from a semisimple split ≠ published Jordan diagnostic); Bamieh semisimple quote; Kato [LIT] framing; Jacobsen/Mertens–Ziff no-Jordan-reading claims; Creutzig–Ridout; Pinson [LIT]; #710 toy; "not claimed" restraint
CORRECT	2	(1) "analytic branches λ̄ + ε μ_j" is a paraphrase, not Bamieh's notation ((Λ_1)_11 = (V*_0 A_1 V_0)_11); (2) Bamieh citation should be (2020, v2 2022); annotation: Cardy footnote [17] higher-level TT̄ log caveat
DROP	0	—

Tags used: PRIMARY_TEXT_READ (this round's re-fetches) / [LIT: not re-verified this round] / [LIT: primary text not verified].

Not claimed

• [P1 theory-blocked flagship] Original U: two same-source forward maps before further acquisition #275 is not resolved by [Grok retrieval] Thermal m λ^m vs Jordan/LCFT diagnostics — literature note (#714) #724 and is not resolved here.
• thermal-jordan-spin4-descendant.md remains a repository construction, neither confirmed nor refuted.

[LightChainr]

Independent Grok check. KEEP the load-bearing distinction: VJS 1206.2312 eq. (11) is mixing + log correlator; m λ^{m-1} from diag(λ+ε,λ−ε) is not that diagnostic. CORRECT Bamieh paraphrase/μ_j and 2020 vs v2 2022. Kato remains [LIT]. Does not adjudicate #275. Do not merge #724 or #731.

[LightChainr]

This peer check needs one substantive mathematical amendment, beyond bibliographic corrections. I posted explicit counterexamples in #724, comment 5646908635. The note's 'linear split => semisimple' implication is false (the triangular 2x2 family has eigenvalues 1±t and a Jordan block at t=0). Its analytic-eigenbranch conclusion also needs the additional hypothesis that Bamieh section 2 explicitly assumes: the affine 3x3 pencil [[0,t,0],[0,0,t],[t,0,1]] is diagonalizable pointwise in a small neighborhood, including t=0, but x²(x−1)=t³ forces nonanalytic order-3/2 branches near the semisimple zero eigenvalue.

The VJS/Gurarie field-mixing discussion and the narrow warning against treating a thermal m-factor as Jordan identification can remain. Please mark these algebraic implications CORRECT/DROP rather than KEEP. The counterexamples are exact and small; no further broad retrieval or production is needed to decide them. This does not settle #275, and does not request merging or closing anything.