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We assume that C is either a *-category (i.e. there is a positive *-operation on the morphisms) or semisimple and spherical over an algebraically closed field F. In the latter case we assume that dim C=sum_i d(X_i)^2 is non-zero, where the summation runs over the isomorphism classes of simple objects. We prove:"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0111205","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"2001-11-19T16:54:20Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"9d791753277aa58d8caa20fdd3e2d4e4595e060f8de7df81058244874e0dcdf4","abstract_canon_sha256":"ab4655b34d2f05c3e4992979f9d567c9fd25c6c3350203784897c5dbe667e75a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:45.772125Z","signature_b64":"/WlhpuDaGzN5i/twQFZ8TnIeo5/D2POnHUL/5DuqmGj0ULnnWyvLdpTFplstHFySh7bkl8ERxmh29MZPDbA6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce132cbe557021b4ac4e53b6455608b5969f52836a2f39d80149b4ddbad86209","last_reissued_at":"2026-07-04T14:35:45.771721Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:45.771721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Subfactors to Categories and Topology II. 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