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Finally, we characterize the moduli of such projectively rigid ttt-∞-categories, demonstrating that the presheaf ∞-category on the 1-dimensional framed cobordism ∞-category serves as the universal projectively rigid ttt-∞-category.","weakest_assumption":"The natural structural condition 'projective rigidity' on t-structured tensor triangulated ∞-categories, which is invoked to establish the analogues of Lazard's theorem, Cohn localizations, and the other main results."}},"verdict_id":"856d9cce-88de-4688-a6b7-bf2736553bfa"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f6bc82d6ce3d42189e202d971cd2643e6c530e0466c0231b25c3716d6a47762a","target":"record","created_at":"2026-06-19T16:10:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1ab08938346c129ea057329532d534d1941360c2930b5725e0b3df7d33a578f2","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-03-29T17:42:38Z","title_canon_sha256":"3620399f849ea8ad402b3fc0f4913ed30159820de19ff05f3b02a03a8da500c9"},"schema_version":"1.0","source":{"id":"2603.27786","kind":"arxiv","version":2}},"canonical_sha256":"273e68519fd921e3137ad2d45b78e4f724b5a2111fb8d68b56408a571647ada6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"273e68519fd921e3137ad2d45b78e4f724b5a2111fb8d68b56408a571647ada6","first_computed_at":"2026-06-19T16:10:36.983791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:36.983791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61o4fzdZaCO20zRQ7Cs/wjmVtUc636YEkvD8v4aOKRadHtroENudEnf6S3Xk3oj2F0rkhG5V1AR7NwkxCs2LDA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:36.984216Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.27786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6bc82d6ce3d42189e202d971cd2643e6c530e0466c0231b25c3716d6a47762a","sha256:bd4851fd77875f2f6d3c88494c6f0c4ce949cbf4917204a8828f0e397b8ca70c"],"state_sha256":"36c49449e57ee374014ce1a75f7034092056f541d8e3d5dde3e83ea57f025710"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PzyRuRr6VZNwmSMrS6HGyCd37jvD7Eva4SS7DugQV24EHlqz0fZKXjnWfAcjnYqTVA8asaltmjPC21ZdDZc1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T01:26:18.253965Z","bundle_sha256":"c49d8a5718c5864f678a5f82c67ab1c06f0154bcbb54831d11dd13c23787431a"}}