feat: triple-mapped S-observable = val-image observable — #2965#2988
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Add triple_map_subtypeUnivEquiv_eq: the observable pushed through Sum.inl, Equiv.Finset.union S Sᶜ, and Equiv.subtypeUnivEquiv equals A.map ⟨Subtype.val,_⟩ (the plain subtype inclusion image of A in V). Via Finset.map_map the three embeddings compose to the inclusion ↥S → V. This identifies the observable of correlation_deleteEdges_straddle_eq_inducedGraph (#2986) with the raw V-vertex observable (e.g. {r,s} for the pair), supplying the observable match for the numeric per-stage increment. Together with deleteEdges_filter_edgeFinset_eq (#2987) and correlation_congr_all (#2986), the remaining gap is only discharging the ball-boundary hypotheses for the straddle-edge finset. Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This was referenced May 26, 2026
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* feat: numeric per-stage correlation increment (Part of #2965) * feat: numeric per-stage correlation increment (Phase A) 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> * docs: fix stale 'not yet formalized' notes per codex (#2989 formalizes the composition) 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 (per-stage increment observable match).
Adds
triple_map_subtypeUnivEquiv_eq(InducedUnion.lean):(((A.map inl).map union).map subtypeUnivEquiv) = A.map ⟨Subtype.val, _⟩. ViaFinset.map_mapthe three embeddings compose to the subtype inclusion↥S → V.This identifies the observable of
correlation_deleteEdges_straddle_eq_inducedGraph(#2986) with the rawV-vertex observable (e.g.{r,s}for the pair), supplying the observable match for the numeric per-stage increment. WithdeleteEdges_filter_edgeFinset_eq(#2987) andcorrelation_congr_all(#2986), the remaining gap to the numeric increment is only the discharge of the ball-boundary hypotheses (hE₀_nd/hE₀_sub/hE₀_sep) for the straddle-edge finset.lake build IsingModel.AmbientLatticeSum.InducedUniongreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code