feat: polymerFreeEnergy < log 2 under (1+t)^|E| < 2 (§18.4 sharpening, Issue #1499) - #1524
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…, Issue #1499) Empty start. Convergence-regime upper bound polymerFreeEnergy < log 2. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
…, Issue #1499) Add `polymerFreeEnergy_lt_log_two_of_pow_lt_two`: in the cluster- expansion convergence regime `(1+t)^|E| < 2` (where the log Taylor expansion converges via PR #1517), the polymer free energy is strictly less than log 2. Proof: combines `polymerFreeEnergy = log(1 + ε(t))` with `ε(t) ≤ (1+t)^|E| - 1 < 1`, giving `1 + ε < 2` and applying `Real.log_lt_log_iff`. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…(§18.4 capstone, Issue #1499) Add `freeEnergy_lt_log_two_plus_high_temp_correction`: under `0 ≤ β·J`, `0 < |ι|`, and `(1+tanh(β·J))^|E| < 2`, freeEnergy G ⟨J, 0, β⟩ < log 2 + (|E|/|ι|) · log cosh(β·J) + log 2 / |ι|. Combines `freeEnergy_eq_polymerFreeEnergy` (Step 612) with the strict bound `polymerFreeEnergy < log 2` (PR #1524). Lifts the polymer-level sharpening to the actual Ising free energy in the cluster-expansion convergence regime. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…(§18.4 capstone, Issue #1499) (#1527) * feat: freeEnergy upper bound in cluster-expansion convergence regime (§18.4 capstone, Issue #1499) Empty start. freeEnergy ≤ log 2 + |E|/|ι| log cosh + log 2 / |ι| under (1+tanh)^|E| < 2. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> * feat: freeEnergy upper bound in cluster-expansion convergence regime (§18.4 capstone, Issue #1499) Add `freeEnergy_lt_log_two_plus_high_temp_correction`: under `0 ≤ β·J`, `0 < |ι|`, and `(1+tanh(β·J))^|E| < 2`, freeEnergy G ⟨J, 0, β⟩ < log 2 + (|E|/|ι|) · log cosh(β·J) + log 2 / |ι|. Combines `freeEnergy_eq_polymerFreeEnergy` (Step 612) with the strict bound `polymerFreeEnergy < log 2` (PR #1524). Lifts the polymer-level sharpening to the actual Ising free energy in the cluster-expansion convergence 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.