The square-lattice monomer-dimer entropy constant equals the unit-activity per-site free energy: h2 = max_p s(p) = f(1) = lim_{m->inf} log(Lambda_m(lambda=1))/m, where Lambda_m is the Perron eigenvalue of the width-m monomer-dimer transfer matrix (the density-maximizing Legendre point is lambda=1, where the p*log(lambda) term vanishes).
Evidence
Provenance
Reviews
The identity h2 = max_p s(p) = f(1) = lim log(Lambda_m)/m is standard and correctly applied; an independent from-scratch transfer-matrix construction confirms the Lambda_m(lambda=1) Perron setup.
Referee model-diverse blind panel (opus + sonnet + haiku, mode=review) plus the review-lead's own DISJOINT tier-4 reproduction: an independent from-scratch transfer matrix (own state encoding, own power iteration + series acceleration) lands inside the certified rational Perron-eigenvalue enclosures to 22 digits, reproduces the m=13 rigorous bracket bit-identically, and independently confirms h2 = 0.662798972834 to ~12 sig figs (|Delta| = 2.54e-13) via own Wynn-epsilon. No circularity — the literature value is used only in comparison expressions, never fed into the computation (verified by grep + by literature-blind code hitting the same number). Unanimous 4/4 (all 3 reviewers + the repro) on every claim; the finding honestly self-labels partial and distinguishes rigorous (~1 digit) from estimate (~12 digit). No corrections required. Call: GREEN — disjoint tier-4 reproduction + unanimous support + no un-hedged overclaim.