[Grok retrieval] Torus rank-2 onset, theta/wedge cores, diamond 3L-1: literature check (#712)

[LightChainr]

Draft. Do not merge. Retrieval-only for issue #712 (parent #650). Single new file: notes/lit-torus-onset-core-20260912.md. Does not touch docs/STATUS.md. No census, no transfer matrix, no Huawei.

Answers to the four questions

1. Wrapping strand = probabilities only. Newman–Ziff (PRIMARY_TEXT_READ), Pruessner–Moloney (PRIMARY_TEXT_READ), LPSA (PRIMARY_TEXT_READ), Pinson (ABSTRACT_ONLY). None classifies minimal occupied sets; the only size-like object in Newman–Ziff is the first-wrapping-n distribution. Pruessner–Moloney's winding-number coexistence rules (primitive classes, incommensurables cannot coexist, one cross-topology cluster) are explicitly heuristic and are the percolation-language echo of the intersection form — not an onset/equality classification.
2. Diamond / tilted / 45° tori: explicit NO. Onset 3L−1 and the 4L² minimizer count do not appear in print. Axis 2L−1 does not either. Akhunzhanov et al. (fetched full text) treat one-direction wrapping only and never state c_L = L or name minimizers — divisibility invariants only.
3. Core classification lives in algebraic topology, as the ticket suspected. Farb–Margalit Primer Ch. 1 (PRIMARY_TEXT_READ): Prop 1.5 (simple closed curves ↔ primitive elements of ℤ²) plus the intersection formulas î = pq′−p′q, i = |pq′−p′q| ⇒ disjoint essential curves are homologous ⇒ a rank-2 spanning pair must intersect ⇒ dumbbell (disjoint cycles) cannot be the core; wedge and theta can. Hatcher (PRIMARY_TEXT_READ) supplies the wedge-of-circles/cycle-rank machinery and shows homotopy alone cannot exclude the dumbbell.
4. Systolic L(|a|+|b|): continuous analogue classical — Loewner's inequality quoted in Ikonen–Marti–Vikman arXiv:2607.22290 (PRIMARY_TEXT_READ), stable norm gives shortest length per integer class on the flat torus. The exact discrete L1 grid statement was not found in print; it is a two-line covering-space net-displacement argument. Simple ⇒ primitive class caveat recorded.

Tripwire (ticket requirement)

• Fetched primary texts: 7 (all tagged); Pinson ABSTRACT_ONLY (Springer/ADS bot-blocked).
• Diamond 3L−1 + 4L² in print: NO.
• No probability paper treated as a configuration classification.

Unique science stays in this PR description; the notes file contains the tagged source ledger. Nothing merged, nothing closed, STATUS untouched.

[LightChainr]

Independent Grok check (not the glm log).

Newman–Ziff wrapping observables are probabilities; that strand does not classify minimal occupied sets. Pruessner–Moloney cond-mat/0310361 exists and is winding probabilities plus a heuristic coexistence rule. Farb–Margalit Prop. 1.5 is the primitive-class bijection on T² (confirmed via independent secondary discussion of that proposition); disjoint essential curves being homologous follows from algebraic intersection 0. Hatcher's graph cycle-rank does not by itself exclude the dumbbell — the note is right that the torus intersection form is the extra input.

KEEP: diamond 3L−1 / 4L² (and axis 2L−1) not found in the wrapping literature; #710's equality classification is not a restatement of NZ/Pinson.

Caveat, not a DROP: LPSA 1992 JSP is planar rectangles; the 1994 BAMS conformal-invariance paper is a different item and was not fetched here. That does not put 3L−1 in print. Pinson remains ABSTRACT_ONLY. I did not independently fetch Ikonen–Marti–Vikman arXiv:2607.22290; Loewner is classical anyway, and the discrete L(|a|+|b|) covering-space bound is elementary.

Do not merge. Do not close #712. Round B (#719–#722) is already running on #715/#717/#718; a derangement for this PR waits until #714 lands.