feat: induced-union splits as disjoint sum under no cross edges — #2965#2977
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Add the structural equality and its correlation factorization: - inducedGraph_sum_map_eq_union_of_no_cross: for disjoint Λ₁,Λ₂ with no G-edge between them, ((inducedGraph Λ₁) ⊕g (inducedGraph Λ₂)).map (union) = inducedGraph (Λ₁ ∪ Λ₂). Upgrades inducedGraph_sum_map_le_union to equality: no cross edges ⇒ every union edge stays within one part. - correlation_inducedGraph_sum_map_inl: an observable supported on Λ₁ has the same correlation in the transported disjoint sum as in inducedGraph Λ₁ (correlation_map_equiv + correlation_sum_inl). Component-factorization bridge from a fully separated (bond-deleted) finite-volume system to the isolated-component correlation. Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This was referenced May 26, 2026
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Part of #2965
Adds the structural component-split equality and its correlation factorization (in
InducedUnion.lean):inducedGraph_sum_map_eq_union_of_no_cross: for disjointΛ₁,Λ₂with noG-edge between them,((inducedGraph Λ₁) ⊕g (inducedGraph Λ₂)).map (union) = inducedGraph (Λ₁ ∪ Λ₂). Upgrades the existinginducedGraph_sum_map_le_union(≤) to equality: with no cross edges, every edge of the induced union stays within one part.correlation_inducedGraph_sum_map_inl: an observable supported onΛ₁has the same correlation in the transported disjoint sum as ininducedGraph Λ₁(viacorrelation_map_equivfeat: correlation invariance under graph isomorphism — #2965 #2976 +correlation_sum_inlfeat: correlation factorization on disjoint sum graph — #2965 #2975).Component-factorization bridge from a fully separated finite-volume system to the isolated-component correlation. (Stating the correlation result directly on
inducedGraph (Λ₁∪Λ₂)would require transporting theFintype edgeSetinstance through the equality — recorded as a follow-up; the equality lemma here makes the graphs coincide.)lake build IsingModel.AmbientLatticeSum.InducedUniongreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code