{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QL7Z5UFBDPOK5OS7KA5G5FA5RS","short_pith_number":"pith:QL7Z5UFB","canonical_record":{"source":{"id":"1204.5807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-04-26T01:54:06Z","cross_cats_sorted":[],"title_canon_sha256":"dc0788d19136523c4975f1a583891e423ecc2e21ad836bacc0e2af96ce806988","abstract_canon_sha256":"c876aeb2068440674b5f575ba3964bac6cc7c5f911c2e6f3f53a691830f0cc2a"},"schema_version":"1.0"},"canonical_sha256":"82ff9ed0a11bdcaeba5f503a6e941d8cb3be4fa2582cf05cfd3e3b44ac04a4bc","source":{"kind":"arxiv","id":"1204.5807","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5807","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5807v1","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5807","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"QL7Z5UFBDPOK","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QL7Z5UFBDPOK5OS7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QL7Z5UFB","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QL7Z5UFBDPOK5OS7KA5G5FA5RS","target":"record","payload":{"canonical_record":{"source":{"id":"1204.5807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-04-26T01:54:06Z","cross_cats_sorted":[],"title_canon_sha256":"dc0788d19136523c4975f1a583891e423ecc2e21ad836bacc0e2af96ce806988","abstract_canon_sha256":"c876aeb2068440674b5f575ba3964bac6cc7c5f911c2e6f3f53a691830f0cc2a"},"schema_version":"1.0"},"canonical_sha256":"82ff9ed0a11bdcaeba5f503a6e941d8cb3be4fa2582cf05cfd3e3b44ac04a4bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:59.485897Z","signature_b64":"ilQEsYzNvAL6lSchps2IUr++mIOIn5afpfQf42CoUT19BcUza6zCDYP/ffG2I2CQ6JW6MT6P4o1tBsh9eTAjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82ff9ed0a11bdcaeba5f503a6e941d8cb3be4fa2582cf05cfd3e3b44ac04a4bc","last_reissued_at":"2026-05-18T03:56:59.484990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:59.484990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.5807","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":"2026-05-18T03:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gWKrT9/HM7dpkaAjT+QUTSmUvIh8zk7nsYxnYNi6vmho45YzCynLu0Dhh9A3jpdz4ZtZfMo9m4szjg0HmaNpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:41:16.392266Z"},"content_sha256":"0fb7017fc396509905244d26a7b59dd5b21b692331bb15fed8e8f324ad5c923c","schema_version":"1.0","event_id":"sha256:0fb7017fc396509905244d26a7b59dd5b21b692331bb15fed8e8f324ad5c923c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QL7Z5UFBDPOK5OS7KA5G5FA5RS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Hopf algebras to tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Agustin Garcia Iglesias, Blas Torrecillas, Cristian Vay, Ivan Angiono, Nicolas Andruskiewitsch","submitted_at":"2012-04-26T01:54:06Z","abstract_excerpt":"This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion subcategory of the non-degenerate quotient of the category of representations of a suitable Hopf algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5807","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":"2026-05-18T03:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KbbhavgAmqzQpfKz32uMw2VOTpRll2KXs+soZSf7Fm8/MlBw7HrdgVWoeDt9vEqfOrVT73kkQWLvEmdwnB2qBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:41:16.392632Z"},"content_sha256":"8590d9e215a09c3a24f6a06a14c4fce7efc90f0485dbf89a9ac55a5eb3221bba","schema_version":"1.0","event_id":"sha256:8590d9e215a09c3a24f6a06a14c4fce7efc90f0485dbf89a9ac55a5eb3221bba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QL7Z5UFBDPOK5OS7KA5G5FA5RS/bundle.json","state_url":"https://pith.science/pith/QL7Z5UFBDPOK5OS7KA5G5FA5RS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QL7Z5UFBDPOK5OS7KA5G5FA5RS/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":"2026-06-23T13:41:16Z","links":{"resolver":"https://pith.science/pith/QL7Z5UFBDPOK5OS7KA5G5FA5RS","bundle":"https://pith.science/pith/QL7Z5UFBDPOK5OS7KA5G5FA5RS/bundle.json","state":"https://pith.science/pith/QL7Z5UFBDPOK5OS7KA5G5FA5RS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QL7Z5UFBDPOK5OS7KA5G5FA5RS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QL7Z5UFBDPOK5OS7KA5G5FA5RS","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":"c876aeb2068440674b5f575ba3964bac6cc7c5f911c2e6f3f53a691830f0cc2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-04-26T01:54:06Z","title_canon_sha256":"dc0788d19136523c4975f1a583891e423ecc2e21ad836bacc0e2af96ce806988"},"schema_version":"1.0","source":{"id":"1204.5807","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5807","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5807v1","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5807","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"QL7Z5UFBDPOK","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QL7Z5UFBDPOK5OS7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QL7Z5UFB","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:8590d9e215a09c3a24f6a06a14c4fce7efc90f0485dbf89a9ac55a5eb3221bba","target":"graph","created_at":"2026-05-18T03:56:59Z","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":"This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion subcategory of the non-degenerate quotient of the category of representations of a suitable Hopf algebra.","authors_text":"Agustin Garcia Iglesias, Blas Torrecillas, Cristian Vay, Ivan Angiono, Nicolas Andruskiewitsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-04-26T01:54:06Z","title":"From Hopf algebras to tensor categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5807","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":"sha256:0fb7017fc396509905244d26a7b59dd5b21b692331bb15fed8e8f324ad5c923c","target":"record","created_at":"2026-05-18T03:56:59Z","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":"c876aeb2068440674b5f575ba3964bac6cc7c5f911c2e6f3f53a691830f0cc2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-04-26T01:54:06Z","title_canon_sha256":"dc0788d19136523c4975f1a583891e423ecc2e21ad836bacc0e2af96ce806988"},"schema_version":"1.0","source":{"id":"1204.5807","kind":"arxiv","version":1}},"canonical_sha256":"82ff9ed0a11bdcaeba5f503a6e941d8cb3be4fa2582cf05cfd3e3b44ac04a4bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82ff9ed0a11bdcaeba5f503a6e941d8cb3be4fa2582cf05cfd3e3b44ac04a4bc","first_computed_at":"2026-05-18T03:56:59.484990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:59.484990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ilQEsYzNvAL6lSchps2IUr++mIOIn5afpfQf42CoUT19BcUza6zCDYP/ffG2I2CQ6JW6MT6P4o1tBsh9eTAjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:59.485897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5807","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fb7017fc396509905244d26a7b59dd5b21b692331bb15fed8e8f324ad5c923c","sha256:8590d9e215a09c3a24f6a06a14c4fce7efc90f0485dbf89a9ac55a5eb3221bba"],"state_sha256":"9a0995f5507890709fa54c51f85b5e73b19025c60614eeb4d58dbcddd21b394d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UzYTmPRGFqndsiuH9iPwE0D9FrzeTUIByUJuKRciINjd5yjfHT7sPRo7YDrShw+oXofTDrwH9pzGzRkWqCL1DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:41:16.394548Z","bundle_sha256":"47a9f7e9aef25273da34abd45af234134b52a0d173323bace80ee02a38a639c8"}}