feat: straddle-set no-cross + not-internal facts — #2965#2982
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Add two graph-level facts about the straddle (cut) edge set of
induce_sum_map_sumCompl_eq_deleteEdges:
- straddle_not_mem_of_same_side: p a ↔ p b ⇒ s(a,b) ∉ straddle (the deleted set
contains no same-side edge), feeding inducedGraph_deleteEdges_eq_of_not_internal.
- deleteEdges_straddle_no_cross: p a, ¬p b ⇒ ¬(G.deleteEdges {straddle}).Adj a b
(the bond-deleted graph disconnects the two sides), the no-cross hypothesis for
correlation_inducedGraph_union_inl_of_no_cross applied to G.deleteEdges {straddle}.
Pure adjacency facts (no Fintype), bridging #2979/#2981/#2978 toward the
bond-deletion → isolated-component capstone via the working inducedGraph route.
Part of #2965
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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…apstone, Finset route) — #2965 (#2983) * feat: bond-deleted correlation = isolated induced subgraph (Finset route) (Part of #2965) * feat: bond-deleted correlation = isolated induced subgraph (Phase A capstone, Finset route) Add correlation_inducedGraph_deleteEdges_union_inl: for S ⊆ W, deleting the cut edges between S and Sᶜ gives correlation (inducedGraph (G.deleteEdges {straddle S}) (S ∪ Sᶜ)) p ((A.map inl).map union) = correlation (inducedGraph G S) p A — the bond-deleted model's correlation of an S-supported observable equals the correlation in the isolated induced subgraph on S of the original model. Assembled from correlation_inducedGraph_union_inl_of_no_cross (#2978) ∘ correlation_congr_of_eq (inducedGraph_deleteEdges_eq_of_not_internal, #2981), with no-cross/not-internal hypotheses discharged by deleteEdges_straddle_no_cross / straddle_not_mem_of_same_side (#2982). Reuses the working inducedGraph/Finset machinery, sidestepping the Equiv.sumCompl instance pathology (#2980) entirely. This is the Issue #2965 Phase A component-factorization capstone: combined with the ball-boundary bond-deletion increment correlation_sub_deleteEdges_le_derivBound (#2974), it yields the per-stage exhaustion increment bound. Part of #2965 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.
Two graph-level facts about the straddle (cut) edge set of
induce_sum_map_sumCompl_eq_deleteEdges(#2979), inSumGraph.lean:straddle_not_mem_of_same_side:p a ↔ p b ⇒ s(a,b) ∉ straddle— feedsinducedGraph_deleteEdges_eq_of_not_internal(feat: inducedGraph unaffected by deleting non-internal edges — #2965 #2981).deleteEdges_straddle_no_cross:p a, ¬p b ⇒ ¬(G.deleteEdges {straddle}).Adj a b— the no-cross hypothesis forcorrelation_inducedGraph_union_inl_of_no_cross(feat: correlation graph-equality congruence + induced-union bridge (union form) — #2965 #2978) applied to the bond-deleted graph.Pure adjacency (no Fintype/instance risk), bridging #2979/#2981/#2978 toward the bond-deletion → isolated-component capstone via the working
inducedGraphroute.lake build IsingModel.SumGraphgreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code