feat: nested-induce correlation transport (whnf wall bypassed) — #2965#2991
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Add correlation_inducedGraph_induce_preimage: correlation companion of inducedGraph_induce_preimage_map_eq (#2990): correlation ((inducedGraph G T).induce {x | x.val ∈ S}) p (A.map nestedSubtypeEquiv.symm) = correlation (inducedGraph G S) p A. The earlier whnf wall (correlation_map_equiv on the nested-subtype graph) is bypassed by applying correlation_map_equiv to the DIRECT graph inducedGraph G S with the inverse relabeling nestedSubtypeEquiv.symm — so the heavy nested-subtype graph appears only as the map RESULT, never as the graph correlation_map_equiv operates on — then bridging via correlation_congr_all and the graph equality #2990. This is the c_k-side identity for the cubic-exhaustion per-stage increment: correlation on inducedGraph (box_k inside box_{k+1}) = correlation on the direct inducedGraph box_k. Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
…w done) Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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…#2992) * feat: two-box per-stage increment (Part of #2965) * Build two-box per-stage increment for cubic exhaustion stages Add `correlation_pair_two_box_le_derivBound`: for nested finsets T₁ ⊆ T₂ and a pair r,s interior to T₁, the pair correlation on the larger box exceeds the one on the smaller box by at most the ball-boundary `derivBound` over the cut edges of the T₁-slice. This is the form instantiated on cubic exhaustion stages box_k ⊆ box_{k+1} to bound the per-stage difference c_{k+1} − c_k (Issue #2965, Phase A). Supporting declarations: - `nestedFinsetEquiv`: the double-subtype relabeling ↥(T₁.subtype (· ∈ T₂)) ≃ ↥T₁. - `correlation_inducedGraph_nested_finset`: concrete-layer companion of `correlation_inducedGraph_induce_preimage` (#2991) using the `Finset.subtype` slice instead of a `Set`-predicate, so it matches the `S : Finset ↥T₂` region of the single-box increment directly and avoids the ↥S vs {x // x.val ∈ T₁} subtype-type mismatch. Composes the single-box increment `correlation_pair_sub_inducedGraph_le_derivBound` (#2989) on G' = inducedGraph G T₂ with the double-induce identification, recovering inducedGraph G T₁ on the inner box. Docs and proof-guide synced. Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com> * Update module doc Main declarations list (codex cross-check) Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>
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Part of #2965 (cubic-exhaustion connection — correlation level).
Adds
correlation_inducedGraph_induce_preimage(InducedUnion.lean), the correlation companion ofinducedGraph_induce_preimage_map_eq(#2990):correlation ((inducedGraph G T).induce {x | x.val ∈ S}) p (A.map nestedSubtypeEquiv.symm) = correlation (inducedGraph G S) p A.The earlier
whnfwall is bypassed: instead of applyingcorrelation_map_equivto the nested-subtype graph (heavy), apply it to the directinducedGraph G Swith the inverse relabelingnestedSubtypeEquiv.symm— so the heavy nested-subtype graph appears only as the map result, never as the graphcorrelation_map_equivoperates on. Then bridge viacorrelation_congr_all+ the graph equality #2990.This is the
c_k-side identity for the cubic-exhaustion per-stage increment. Combined with #2989 (the abstract per-stage increment), the cubic-exhaustion instantiationc_{k+1}−c_k ≤ derivBound(shell)is now within reach.lake build IsingModel.AmbientLatticeSum.InducedUniongreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code