{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LO3ZZ7DUYPWA7E2T6MUIKGLWAU","short_pith_number":"pith:LO3ZZ7DU","canonical_record":{"source":{"id":"1701.00097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-31T13:04:03Z","cross_cats_sorted":[],"title_canon_sha256":"1d818cc031d4b96d055ef015909ee266298fd685b9e7f050c6c97acc753b3453","abstract_canon_sha256":"be39b893e0df24a48863ed0765095edaedfe96f76c28bc7d95f23285422e7293"},"schema_version":"1.0"},"canonical_sha256":"5bb79cfc74c3ec0f9353f328851976051da33ecde9849643a8018edaace121d2","source":{"kind":"arxiv","id":"1701.00097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00097","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00097v1","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00097","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"LO3ZZ7DUYPWA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LO3ZZ7DUYPWA7E2T","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LO3ZZ7DU","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LO3ZZ7DUYPWA7E2T6MUIKGLWAU","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-31T13:04:03Z","cross_cats_sorted":[],"title_canon_sha256":"1d818cc031d4b96d055ef015909ee266298fd685b9e7f050c6c97acc753b3453","abstract_canon_sha256":"be39b893e0df24a48863ed0765095edaedfe96f76c28bc7d95f23285422e7293"},"schema_version":"1.0"},"canonical_sha256":"5bb79cfc74c3ec0f9353f328851976051da33ecde9849643a8018edaace121d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:36.380870Z","signature_b64":"ljCGHiTa7230eAr/ECECBVbQrUOKN0PCCK5vzJHBF6gkGDFl2L2DGiJR1HvgVRYrL+qyErtYibqfn1VEHIdqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bb79cfc74c3ec0f9353f328851976051da33ecde9849643a8018edaace121d2","last_reissued_at":"2026-05-18T00:53:36.380283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:36.380283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00097","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PrXj41YEYYLhetT1gguE9ptE6kIval5507ksFU2sH3vJCG6H95LU1a1wCzFaoSki/k2kvrsWZgyD33lH8+IUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:56:37.127101Z"},"content_sha256":"0968555a228405a1c0f18b9e3e3e3a26a60d73ac0788247bd29bd046e76535db","schema_version":"1.0","event_id":"sha256:0968555a228405a1c0f18b9e3e3e3a26a60d73ac0788247bd29bd046e76535db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LO3ZZ7DUYPWA7E2T6MUIKGLWAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tube algebra of group-type subfactors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Dietmar Bisch, Narayan Rakshit, Paramita Das, Shamindra Kumar Ghosh","submitted_at":"2016-12-31T13:04:03Z","abstract_excerpt":"We describe the tube algebra and its representations in the cases of diagonal and Bisch-Haagerup subfactors possibly with a scalar 3-cocycle obstruction. We show that these categories are additively equivalent to the direct product over conjugacy classes of representation category of a centralizer subgroup (corresponding to the conjugacy class) twisted by a scalar 2-cocycle obtained from the 3-cocycle obstruction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00097","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptUmFPOLDQvlXVTWla8nJacDCLYPOR8ARHd11dFxBmWoSQfsqMSzkBlDYzDga2haCJvhcfPGWolEd10+wcUwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:56:37.127466Z"},"content_sha256":"0abaf40a15443e343a55c74a0b6b7a55379289cf9c3c988b0648819e68cb3f75","schema_version":"1.0","event_id":"sha256:0abaf40a15443e343a55c74a0b6b7a55379289cf9c3c988b0648819e68cb3f75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LO3ZZ7DUYPWA7E2T6MUIKGLWAU/bundle.json","state_url":"https://pith.science/pith/LO3ZZ7DUYPWA7E2T6MUIKGLWAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LO3ZZ7DUYPWA7E2T6MUIKGLWAU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T12:56:37Z","links":{"resolver":"https://pith.science/pith/LO3ZZ7DUYPWA7E2T6MUIKGLWAU","bundle":"https://pith.science/pith/LO3ZZ7DUYPWA7E2T6MUIKGLWAU/bundle.json","state":"https://pith.science/pith/LO3ZZ7DUYPWA7E2T6MUIKGLWAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LO3ZZ7DUYPWA7E2T6MUIKGLWAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LO3ZZ7DUYPWA7E2T6MUIKGLWAU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"be39b893e0df24a48863ed0765095edaedfe96f76c28bc7d95f23285422e7293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-31T13:04:03Z","title_canon_sha256":"1d818cc031d4b96d055ef015909ee266298fd685b9e7f050c6c97acc753b3453"},"schema_version":"1.0","source":{"id":"1701.00097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00097","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00097v1","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00097","created_at":"2026-05-18T00:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"LO3ZZ7DUYPWA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LO3ZZ7DUYPWA7E2T","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LO3ZZ7DU","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:0abaf40a15443e343a55c74a0b6b7a55379289cf9c3c988b0648819e68cb3f75","target":"graph","created_at":"2026-05-18T00:53:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We describe the tube algebra and its representations in the cases of diagonal and Bisch-Haagerup subfactors possibly with a scalar 3-cocycle obstruction. We show that these categories are additively equivalent to the direct product over conjugacy classes of representation category of a centralizer subgroup (corresponding to the conjugacy class) twisted by a scalar 2-cocycle obtained from the 3-cocycle obstruction.","authors_text":"Dietmar Bisch, Narayan Rakshit, Paramita Das, Shamindra Kumar Ghosh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-31T13:04:03Z","title":"Tube algebra of group-type subfactors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00097","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0968555a228405a1c0f18b9e3e3e3a26a60d73ac0788247bd29bd046e76535db","target":"record","created_at":"2026-05-18T00:53:36Z","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":"be39b893e0df24a48863ed0765095edaedfe96f76c28bc7d95f23285422e7293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-31T13:04:03Z","title_canon_sha256":"1d818cc031d4b96d055ef015909ee266298fd685b9e7f050c6c97acc753b3453"},"schema_version":"1.0","source":{"id":"1701.00097","kind":"arxiv","version":1}},"canonical_sha256":"5bb79cfc74c3ec0f9353f328851976051da33ecde9849643a8018edaace121d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bb79cfc74c3ec0f9353f328851976051da33ecde9849643a8018edaace121d2","first_computed_at":"2026-05-18T00:53:36.380283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:36.380283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ljCGHiTa7230eAr/ECECBVbQrUOKN0PCCK5vzJHBF6gkGDFl2L2DGiJR1HvgVRYrL+qyErtYibqfn1VEHIdqAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:36.380870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0968555a228405a1c0f18b9e3e3e3a26a60d73ac0788247bd29bd046e76535db","sha256:0abaf40a15443e343a55c74a0b6b7a55379289cf9c3c988b0648819e68cb3f75"],"state_sha256":"810a389b74ed30f6c3b639f2d62cce55dee32520898aa8d3c44ae81b2080ffbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FEZCSt5z5BlpQHPp2bBHzI1yDa0rVvgZzIEgAfBtGj/p7RDMvqHPe5IBxCBTgIf3NJD5HA7zq7PBVofHulWcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:56:37.129513Z","bundle_sha256":"623bcacbaaabaa8935b122fb1162659f8e86d47610020ac55da9c00e4d76c0ff"}}