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Retrieval: torus wrapping probabilities vs the matching function (#642) - #654

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Retrieval: torus wrapping probabilities vs the matching function (#642)#654
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Cite-or-gap for #642 Q1–Q5, at first hand where the PDFs/HTML were opened this session.

  • Q2/Q3 are cites, not gaps. Mertens–Ziff PRE 94, 062152 (2016) is the repository matching function: M = R^x − R̂^x(1−p) for x ∈ {c,b,e,h}, exact at every finite L. The unique root tends to p_c; the L^{-4} rate is empirical, not a theorem.
  • Q1: Pinson wrapping types via Newman–Ziff (13)–(15) and Pruessner–Moloney. Universal at criticality; they transfer to square site; matching-lattice wrapping is not in those tables.
  • Q4: wrapping R_L(p_c)−R_∞ ∼ L^{-2} (conjecture, NZ); matching-root ∼ L^{-4} (empirical, MZ/Jacobsen). Projected shape ω ≈ 0.97 is a gap relative to this literature.
  • Q5: Pinson π({1,0}) ratio 2.969 at r=2 exists and does not, without a new identification, predict the matching-odd aspect ladder ([Compute] Put the wrapping channel on published ground before the next ladder #576 non-claim kept).

Does not close #642. Does not edit docs/STATUS.md. Pinson 1994 JSP itself was not opened as a PDF; formulae are quoted from Newman–Ziff and Pruessner–Moloney.

Related: #640, #635, #618, #633, PR #653.

…).

Q1-Q5 against Pinson (via Newman-Ziff / Pruessner-Moloney), Mertens-Ziff
2016, and the L=3,4 census. The finite matching identity is published;
the projected shape exponent is not. Does not close #642 or edit STATUS.
Fold bibliographic corrections from PR #656 (Pinson 1167-1177, no arXiv)
and four extra entries. Axis L=5 / diamond L=4 K2 five-cell support is
now recorded as verification of the published pairing, not a gap.
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Updated: Pinson page range 1167–1177 / no arXiv (from #656); Q2 notation trap (\hat R(1-p)) = vacant matching wrap at equal (p); L=5 and diamond L=4 K2 recorded as five-cell verification of the published pairing. Extra bib entries from #656 folded in.

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[Grok / deep retrieval] Torus wrapping probabilities: the exact results, their sector structure, and what is known about primal-versus-matching

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