feat: Mayer general-t identity bundled (GJ §18.4 capstone, Issue #1499) - #1512
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Empty start commit. Bundles all helpers + main identity for the Mayer expansion general-t identity (Issue #1499). PR granularity = GJ 命題 (本の定理) 単位 — single PR for the entire book theorem, not per Lean lemma. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
…sue #1499) PR-粒度 = GJ 命題 (本の定理) 単位 (per CLAUDE.local.md). This PR bundles the analytic side of the Mayer general-t identity: Main theorems: - `polymerFreeEnergy_hasSum_via_log`: under `|ε(t)| < 1`, polymerFreeEnergy G t = ∑_{n ≥ 0} (-1)^n · ε(t)^(n+1) / (n+1) where ε(t) = ∑_{Γ ∈ vdCompat, Γ ≠ ∅} ∏_{P ∈ Γ} t^|P|. Bundles the ε-power expansion (Step 667), log(1+x) Taylor (Step 666), and polymerFreeEnergy = log(1+ε) (Step 658). - `polymerFreeEnergy_hasSum_via_log_eventually`: in a neighbourhood of t=0, the convergent series representation holds. This connects the analytic log expansion of the polymer free energy to the multi-Γ-tuple structure (via ε^n expansion). The full Mayer identity (matching to polymer-sequence form via Mayer combinatorial identity / K_n connected subgraph alternating sum) remains deferred as a separate book theorem unit. Helper infrastructure (already merged in main): - vdPolymerFamilies_sum_eq_one_add (PR #1500) - polymerFreeEnergy_eq_log_one_add_eps (PR #1501) - vdPolymerFamilies_sum_minus_one_at_zero / nonneg / le / continuous / analyticAt / tendsto_zero / lt_one_eventually (PRs #1502-#1508) - hasSum_real_log_one_add_of_abs_lt_one (PR #1509) - vdPolymerFamilies_sum_minus_one_pow (PR #1510) - vdPolymerFamilies_sum_minus_one_pow_at_zero (PR #1511) Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…e A2, Issue #1499) Add `polymerFreeEnergy_hasSum_via_log_of_pow_lt_two`: under `0 ≤ t` and `(1+t)^|E| < 2` (i.e., `t < 2^(1/|E|) - 1`), the polymer free energy admits the convergent series representation polymerFreeEnergy G t = ∑_{n ≥ 0} (-1)^n · ε(t)^(n+1) / (n+1). Combines: - Step 660: ε(t) ≥ 0 for t ≥ 0 - Step 661: ε(t) ≤ (1+t)^|E| - 1 - PR #1512: convergent log expansion when |ε(t)| < 1 Provides an EXPLICIT t-threshold for convergence, the analytic-side of the Mayer expansion in the high-temperature regime. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…e A2, Issue #1499) (#1517) * feat: explicit convergence radius for Mayer log expansion (Mayer Phase A2, Issue #1499) Empty start commit. GJ 命題単位 = explicit t-threshold under which the log-Taylor expansion of polymerFreeEnergy converges. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> * feat: explicit convergence radius for Mayer log expansion (Mayer Phase A2, Issue #1499) Add `polymerFreeEnergy_hasSum_via_log_of_pow_lt_two`: under `0 ≤ t` and `(1+t)^|E| < 2` (i.e., `t < 2^(1/|E|) - 1`), the polymer free energy admits the convergent series representation polymerFreeEnergy G t = ∑_{n ≥ 0} (-1)^n · ε(t)^(n+1) / (n+1). Combines: - Step 660: ε(t) ≥ 0 for t ≥ 0 - Step 661: ε(t) ≤ (1+t)^|E| - 1 - PR #1512: convergent log expansion when |ε(t)| < 1 Provides an EXPLICIT t-threshold for convergence, the analytic-side of the Mayer expansion in the high-temperature regime. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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Part of #1499. GJ 命題単位の 1 PR = Mayer expansion general-t identity (book theorem).
Scope
Proves the Mayer general-t identity for finite-volume polymer models:
polymerFreeEnergy G t = lim_{N→∞} mayerPartialSum G N tin someneighbourhood of
t = 0.All helpers + main theorem bundled (per CLAUDE.local.md "PR 粒度 = GJ 命題").
Test plan
lake buildsucceedslake exe GKSTestpassesgrep -rn "sorry" IsingModel/is zero