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reduction_exists.py: every disk with k>=1 (and every irreducible disk) has a Phi-NON-INCREASING vertex removal (|Phi(D-v)| <= |Phi(D)|), 100% over thousands of disks -- so induction to the k=0 base case is viable. BUT the clean set-inclusion Phi(D-v) subset Phi(D) holds for only ~8%, so the size step cannot be proved by "re-inserting v loses no sequence"; it needs a genuine cardinality injection between non-nested sets. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>