{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FNRUPKAJVUZUSUIINYMWOMYHHD","short_pith_number":"pith:FNRUPKAJ","schema_version":"1.0","canonical_sha256":"2b6347a809ad334951086e1967330738eb09971d714240a69cddb0eea5ac2c58","source":{"kind":"arxiv","id":"1308.5723","version":1},"attestation_state":"computed","paper":{"title":"Fusion categories between $C \\boxtimes D$ and $C * D$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.OA","authors_text":"David Penneys, Masaki Izumi, Scott Morrison","submitted_at":"2013-08-27T00:21:16Z","abstract_excerpt":"Given a pair of fusion categories $C$ and $D$, we may form the free product $C * D$ and the tensor product $C \\boxtimes D$. It is natural to think of the tensor product as a quotient of the free product. What other quotients are possible?\n  When $C=D=A_2$, there is an infinite family of quotients interpolating between the free product and the tensor product (closely related to the $A_{2n-1}^{(1)}$ and $D_{n+2}^{(1)}$ subfactors at index 4). Bisch and Haagerup discovered one example of such an intermediate quotient when $C=A_2$ and $D=T_2$, and suggested that there might be another family here."},"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":"1308.5723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-08-27T00:21:16Z","cross_cats_sorted":["math.CT","math.QA"],"title_canon_sha256":"dec2bc29f6a42f98b0f44cc16597fc87a2fc1e57193af858407ea0ef5a821301","abstract_canon_sha256":"e34679f4d1fcfa112d048b4fe5cb81c7c6b84b28c4a70c8daec3083fe80ab83a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:51.462231Z","signature_b64":"fv0RQM/TwTLAFI3zwcktcpEb5vJNmO1eQ6cnNmHDKyEFD9Oj5sh719TBGrk3aLMP/hEhxTPi3vOENeeV8GJbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b6347a809ad334951086e1967330738eb09971d714240a69cddb0eea5ac2c58","last_reissued_at":"2026-05-18T03:14:51.461337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:51.461337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fusion categories between $C \\boxtimes D$ and $C * D$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.OA","authors_text":"David Penneys, Masaki Izumi, Scott Morrison","submitted_at":"2013-08-27T00:21:16Z","abstract_excerpt":"Given a pair of fusion categories $C$ and $D$, we may form the free product $C * D$ and the tensor product $C \\boxtimes D$. It is natural to think of the tensor product as a quotient of the free product. What other quotients are possible?\n  When $C=D=A_2$, there is an infinite family of quotients interpolating between the free product and the tensor product (closely related to the $A_{2n-1}^{(1)}$ and $D_{n+2}^{(1)}$ subfactors at index 4). Bisch and Haagerup discovered one example of such an intermediate quotient when $C=A_2$ and $D=T_2$, and suggested that there might be another family here."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5723","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":"1308.5723","created_at":"2026-05-18T03:14:51.461493+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.5723v1","created_at":"2026-05-18T03:14:51.461493+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5723","created_at":"2026-05-18T03:14:51.461493+00:00"},{"alias_kind":"pith_short_12","alias_value":"FNRUPKAJVUZU","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FNRUPKAJVUZUSUII","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FNRUPKAJ","created_at":"2026-05-18T12:27:45.050594+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/FNRUPKAJVUZUSUIINYMWOMYHHD","json":"https://pith.science/pith/FNRUPKAJVUZUSUIINYMWOMYHHD.json","graph_json":"https://pith.science/api/pith-number/FNRUPKAJVUZUSUIINYMWOMYHHD/graph.json","events_json":"https://pith.science/api/pith-number/FNRUPKAJVUZUSUIINYMWOMYHHD/events.json","paper":"https://pith.science/paper/FNRUPKAJ"},"agent_actions":{"view_html":"https://pith.science/pith/FNRUPKAJVUZUSUIINYMWOMYHHD","download_json":"https://pith.science/pith/FNRUPKAJVUZUSUIINYMWOMYHHD.json","view_paper":"https://pith.science/paper/FNRUPKAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.5723&json=true","fetch_graph":"https://pith.science/api/pith-number/FNRUPKAJVUZUSUIINYMWOMYHHD/graph.json","fetch_events":"https://pith.science/api/pith-number/FNRUPKAJVUZUSUIINYMWOMYHHD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FNRUPKAJVUZUSUIINYMWOMYHHD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FNRUPKAJVUZUSUIINYMWOMYHHD/action/storage_attestation","attest_author":"https://pith.science/pith/FNRUPKAJVUZUSUIINYMWOMYHHD/action/author_attestation","sign_citation":"https://pith.science/pith/FNRUPKAJVUZUSUIINYMWOMYHHD/action/citation_signature","submit_replication":"https://pith.science/pith/FNRUPKAJVUZUSUIINYMWOMYHHD/action/replication_record"}},"created_at":"2026-05-18T03:14:51.461493+00:00","updated_at":"2026-05-18T03:14:51.461493+00:00"}