{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:R3NPYS3UBG2P673K7YF3HYQ4R6","short_pith_number":"pith:R3NPYS3U","schema_version":"1.0","canonical_sha256":"8edafc4b7409b4ff7f6afe0bb3e21c8f83331dbfeb6f77ded85a68276f31cf96","source":{"kind":"arxiv","id":"math/0101099","version":1},"attestation_state":"computed","paper":{"title":"Continuous Fields of $C^*$-Algebras Arising from Extensions of Tensor $C^*$-Categories","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ezio Vasselli","submitted_at":"2001-01-11T14:33:55Z","abstract_excerpt":"The notion of extension of a given $C^*$-category $C$ by a $C^*$-algebra $A$ is introduced. In the commutative case $A = C(\\Omega)$, the objects of the extension category are interpreted as fiber bundles over $\\Omega$ of objects belonging to the initial category. It is shown that the Doplicher-Roberts algebra (DR-algebra in the following) associated to an object in the extension of a strict tensor $C^*$-category is a continuous field of DR-algebras coming from the initial one. In the case of the category of the hermitian vector bundles over $\\Omega$ the general result implies that the DR-algeb"},"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/0101099","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2001-01-11T14:33:55Z","cross_cats_sorted":[],"title_canon_sha256":"52f90a6cae0e6ae6e2817d25a8b6c2d26665d561ab7a824f40a0271254c4d89d","abstract_canon_sha256":"b37ac035032d8f6f2a717ef3e50016484184106df1646e3aebe191bf85e9a7f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:05.455336Z","signature_b64":"ZlRtFLqPkN51UPPaFDz1qv6s5GYnFW/nu8o3VHoOSQoruw4fOYHNH+t3RIyUv2JSL3/rq/v9tTv6S+gqbc8GBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8edafc4b7409b4ff7f6afe0bb3e21c8f83331dbfeb6f77ded85a68276f31cf96","last_reissued_at":"2026-05-18T04:08:05.454641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:05.454641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuous Fields of $C^*$-Algebras Arising from Extensions of Tensor $C^*$-Categories","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ezio Vasselli","submitted_at":"2001-01-11T14:33:55Z","abstract_excerpt":"The notion of extension of a given $C^*$-category $C$ by a $C^*$-algebra $A$ is introduced. In the commutative case $A = C(\\Omega)$, the objects of the extension category are interpreted as fiber bundles over $\\Omega$ of objects belonging to the initial category. It is shown that the Doplicher-Roberts algebra (DR-algebra in the following) associated to an object in the extension of a strict tensor $C^*$-category is a continuous field of DR-algebras coming from the initial one. In the case of the category of the hermitian vector bundles over $\\Omega$ the general result implies that the DR-algeb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101099","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0101099","created_at":"2026-05-18T04:08:05.454725+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0101099v1","created_at":"2026-05-18T04:08:05.454725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101099","created_at":"2026-05-18T04:08:05.454725+00:00"},{"alias_kind":"pith_short_12","alias_value":"R3NPYS3UBG2P","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"R3NPYS3UBG2P673K","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"R3NPYS3U","created_at":"2026-05-18T12:25:50.845339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6","json":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6.json","graph_json":"https://pith.science/api/pith-number/R3NPYS3UBG2P673K7YF3HYQ4R6/graph.json","events_json":"https://pith.science/api/pith-number/R3NPYS3UBG2P673K7YF3HYQ4R6/events.json","paper":"https://pith.science/paper/R3NPYS3U"},"agent_actions":{"view_html":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6","download_json":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6.json","view_paper":"https://pith.science/paper/R3NPYS3U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0101099&json=true","fetch_graph":"https://pith.science/api/pith-number/R3NPYS3UBG2P673K7YF3HYQ4R6/graph.json","fetch_events":"https://pith.science/api/pith-number/R3NPYS3UBG2P673K7YF3HYQ4R6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6/action/storage_attestation","attest_author":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6/action/author_attestation","sign_citation":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6/action/citation_signature","submit_replication":"https://pith.science/pith/R3NPYS3UBG2P673K7YF3HYQ4R6/action/replication_record"}},"created_at":"2026-05-18T04:08:05.454725+00:00","updated_at":"2026-05-18T04:08:05.454725+00:00"}