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Invariant: At depth pos, path contains exactly pos distinct indices, used matches path exactly, and equal values at one level expand through only their canonical representative.

candidate confidence: 0.565 · metadata_only

Invariant: Every uneliminated pair uses endpoints inside [l,r]; a moved endpoint is proven unable to pair with any remaining opposite endpoint to satisfy the goal.

candidate confidence: 0.452 · metadata_only

Invariant: After processing a[0:read], a[0:write] is exactly its correct stable filtered output, with write no farther than read+1.

candidate confidence: 0.434 · metadata_only