Retrieval: torus wrapping probabilities vs the matching function (#642) - #654
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Retrieval: torus wrapping probabilities vs the matching function (#642)#654LightChainr wants to merge 2 commits into
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…). 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.
This was referenced Sep 8, 2026
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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This was referenced Sep 8, 2026
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Cite-or-gap for #642 Q1–Q5, at first hand where the PDFs/HTML were opened this session.
M = R^x − R̂^x(1−p)forx ∈ {c,b,e,h}, exact at every finite L. The unique root tends top_c; theL^{-4}rate is empirical, not a theorem.R_L(p_c)−R_∞ ∼ L^{-2}(conjecture, NZ); matching-root∼ L^{-4}(empirical, MZ/Jacobsen). Projected shapeω ≈ 0.97is a gap relative to this literature.π({1,0})ratio 2.969 atr=2exists 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.