feat: freeEnergy jointly AnalyticOnNhd ℝ _ Set.univ (§18.6 capstone, Issue #1499) - #1532
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… Issue #1499) Empty start. Global form of jointly analyticAt. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
… Issue #1499) Add `partitionFunction_analyticOnNhd_joint` and `freeEnergy_analyticOnNhd_joint`: global forms of PR #1531's per-point joint analyticity. The functions `(β, J, h) ↦ Z(β, J, h)` and `(β, J, h) ↦ f(β, J, h)` are `AnalyticOnNhd ℝ _ Set.univ` jointly across all of ℝ × ℝ × ℝ. Completes the §18.6 capstone in its strongest form: free energy is jointly real-analytic in all three Ising parameters at every point. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…8.6, Issue #1499) Add four direct corollaries of joint analyticity (PRs #1531, #1532): - `partitionFunction_continuous_joint`: Z is Continuous in (β, J, h). - `partitionFunction_differentiable_joint`: Z is Differentiable ℝ in (β, J, h). - `freeEnergy_continuous_joint`: f is Continuous in (β, J, h). - `freeEnergy_differentiable_joint`: f is Differentiable ℝ in (β, J, h). All follow from `AnalyticAt → ContinuousAt → Continuous` and `AnalyticAt → DifferentiableAt → Differentiable`, applied pointwise. Completes the regularity hierarchy for the §18.6 capstone in joint form: Continuous ⊆ Differentiable ⊆ AnalyticAt (per-point) ⊆ AnalyticOnNhd ℝ _ Set.univ (global). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…8.6, Issue #1499) (#1533) * feat: freeEnergy jointly Continuous + Differentiable in (β, J, h) (§18.6, Issue #1499) Empty start. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> * feat: freeEnergy jointly Continuous + Differentiable in (β, J, h) (§18.6, Issue #1499) Add four direct corollaries of joint analyticity (PRs #1531, #1532): - `partitionFunction_continuous_joint`: Z is Continuous in (β, J, h). - `partitionFunction_differentiable_joint`: Z is Differentiable ℝ in (β, J, h). - `freeEnergy_continuous_joint`: f is Continuous in (β, J, h). - `freeEnergy_differentiable_joint`: f is Differentiable ℝ in (β, J, h). All follow from `AnalyticAt → ContinuousAt → Continuous` and `AnalyticAt → DifferentiableAt → Differentiable`, applied pointwise. Completes the regularity hierarchy for the §18.6 capstone in joint form: Continuous ⊆ Differentiable ⊆ AnalyticAt (per-point) ⊆ AnalyticOnNhd ℝ _ Set.univ (global). 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. Global form of PR #1531.