feat: bond-deleted raw correlation = isolated induced subgraph (per-stage increment form) — #2965#2986
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…tage increment form)
Add two lemmas closing the Phase A per-stage-increment assembly:
- correlation_congr_all: G₁ = G₂ ⇒ correlation G₁ = correlation G₂ across ALL
instances (vertex Fintype + edgeSet Fintype), since Fintype is Subsingleton
(Fintype.subsingleton). Strengthens correlation_congr_of_eq; resolves the
vertex-Fintype diamond between Finset.Subtype.fintype (inducedGraph) and the
Set-induce vertex Fintype.
- correlation_deleteEdges_straddle_eq_inducedGraph: the raw bond-deleted graph's
correlation of an S-supported observable equals the isolated induced-subgraph
correlation:
correlation (G.deleteEdges {straddle S}) p (((A.map inl).map union).map subtypeUnivEquiv)
= correlation (inducedGraph G S) p A
Composes correlation_induce_of_forall_mem (on ↑(S∪Sᶜ)) ∘ correlation_congr_all
∘ correlation_inducedGraph_deleteEdges_union_inl.
This is the per-stage-increment form that pairs directly with the ball-boundary
bond-deletion increment correlation_sub_deleteEdges_le_derivBound (#2974).
Part of #2965
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
… formalized) Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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Part of #2965. Closes the Phase A per-stage-increment assembly, resolving the vertex-
Fintypediamond flagged earlier.correlation_congr_all:G₁ = G₂ ⇒ correlation G₁ = correlation G₂across all instances (vertexFintype+edgeSet Fintype), sinceFintypeisSubsingleton(Fintype.subsingleton). Strengthenscorrelation_congr_of_eq(feat: correlation graph-equality congruence + induced-union bridge (union form) — #2965 #2978).correlation_deleteEdges_straddle_eq_inducedGraph:correlation (G.deleteEdges {straddle S}) p (((A.map inl).map union).map subtypeUnivEquiv) = correlation (inducedGraph G S) p A— the raw bond-deleted graph's correlation of anS-supported observable equals the isolated induced-subgraph correlation. Composescorrelation_induce_of_forall_mem(feat: generalize induce-univ correlation to any full set — #2965 #2985) ∘correlation_congr_all∘correlation_inducedGraph_deleteEdges_union_inl(feat: bond-deleted correlation = isolated induced subgraph (Phase A capstone, Finset route) — #2965 #2983).Pairs directly with the ball-boundary bond-deletion increment
correlation_sub_deleteEdges_le_derivBound(#2974) → per-stage exhaustion increment bound.lake build IsingModel.AmbientLatticeSum.InducedUniongreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code