feat: numeric per-stage correlation increment (Phase A) — #2965#2989
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Add correlation_pair_sub_inducedGraph_le_derivBound (new PerStageIncrement.lean):
for r,s ∈ S, r≠s, ferromagnetic, h=0, and r,s not on any cut (straddle) edge,
correlation G p {r,s} − correlation (inducedGraph G S) p {⟨r,_⟩,⟨s,_⟩}
≤ derivBound G (G.edgeFinset.filter straddle) p r s.
The full-model pair correlation exceeds the isolated induced-subgraph pair
correlation by at most the ball-boundary derivBound over the cut edges.
Composes the ball-boundary bond-deletion increment
correlation_sub_deleteEdges_le_derivBound (#2974) with the component-factorization
bridge correlation_deleteEdges_straddle_eq_inducedGraph (#2986), via
deleteEdges_filter_edgeFinset_eq (#2987) + correlation_congr_all +
triple_map_subtypeUnivEquiv_eq (#2988). The straddle predicate is @[reducible]
(to match the inline straddle set of the component lemmas under unification) and
the graph/observable bridge is a separate lemma (correlation_deleteEdges_filter_pair_eq)
to keep elaboration within the heartbeat budget.
Part of #2965
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
…s the composition) Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This was referenced May 26, 2026
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* feat: nested induced-subgraph graph equality (Part of #2965) * feat: nested induced-subgraph graph equality Add nestedSubtypeEquiv and inducedGraph_induce_preimage_map_eq: for S ⊆ T, ((inducedGraph G T).induce {x : ↥T | x.val ∈ S}).map nestedSubtypeEquiv = inducedGraph G S — inducing box_k inside inducedGraph G box_{k+1} equals, up to the nested-subtype relabeling {x : ↥T // x.val ∈ S} ≃ ↥S, the direct induced subgraph on S. An edge survives iff its deep endpoints are G-adjacent and both in S. Graph-level foundation for instantiating the per-stage increment (correlation_pair_sub_inducedGraph_le_derivBound, #2989) on cubic exhaustion stages box_k ⊆ box_{k+1}. The correlation-level transport across this iso is a follow-up (it currently hits a whnf elaboration wall in correlation_map_equiv on the nested-subtype graph, needing a lighter sum-level encoding). 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. Closes the numeric per-stage increment — the culmination of the Phase A component-factorization bridge.
Adds
correlation_pair_sub_inducedGraph_le_derivBound(newPerStageIncrement.lean, importsWeakBound+InducedUnion): forr,s ∈ S,r≠s, ferromagnetic,h=0, andr,snot on any cut edge,correlation G p {r,s} − correlation (inducedGraph G S) p {⟨r,_⟩,⟨s,_⟩} ≤ derivBound G (G.edgeFinset.filter straddle) p r s.Composes #2974 (ball-boundary bond-deletion increment) with #2986 (component-factorization bridge) via #2987 (Finset↔Set deletion) +
correlation_congr_all+ #2988 (observable identity).Elaboration-performance resolution (the earlier monolithic
calctimed out): the straddle predicate is@[reducible](matches the inline straddle set of the component lemmas under unification), and the graph/observable bridge is a separate lemma to keep each elaboration within the heartbeat budget.lake build IsingModel.AmbientLatticeSum.PerStageIncrementgreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code