feat: bond-deleted correlation = isolated induced subgraph (Phase A capstone, Finset route) — #2965#2983
Merged
Conversation
…apstone, 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>
This was referenced May 26, 2026
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Part of #2965. Resolves the Phase A component-factorization capstone that was blocked by the
Equiv.sumComplinstance pathology (#2980), via the workinginducedGraph/Finset route.Adds
correlation_inducedGraph_deleteEdges_union_inl(InducedUnion.lean): forS ⊆ W,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 onSof the original model.Assembled from:
correlation_inducedGraph_union_inl_of_no_cross(feat: correlation graph-equality congruence + induced-union bridge (union form) — #2965 #2978) — no cross edges in the bond-deleted graph (deleteEdges_straddle_no_cross, feat: straddle-set no-cross + not-internal facts — #2965 #2982)correlation_congr_of_eqofinducedGraph_deleteEdges_eq_of_not_internal(feat: inducedGraph unaffected by deleting non-internal edges — #2965 #2981) — deleting the cut leaves the within-Sinduced subgraph unchanged (straddle_not_mem_of_same_side, feat: straddle-set no-cross + not-internal facts — #2965 #2982)Combined with the ball-boundary bond-deletion increment
correlation_sub_deleteEdges_le_derivBound(#2974), this yields the per-stage exhaustion increment bound.lake build IsingModel.AmbientLatticeSum.InducedUniongreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code