{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:55ZCTPLG33XDWRSRNL7MO3MTDW","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":"2dc7c1f01cd569503671284486108bd3cf3bf5ce193fcf75da644f214c9fd28f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-09-10T10:15:15Z","title_canon_sha256":"4fa4005e683b32e30c4a83f417a61e544c6b3f05254c343ceb42dbd01aed683e"},"schema_version":"1.0","source":{"id":"1609.03023","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03023","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03023v1","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03023","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"55ZCTPLG33XD","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"55ZCTPLG33XDWRSR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"55ZCTPLG","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:5f1c91cc8fc096999652252170095fbf556821cb2fe0d236a7b3205f741f985b","target":"graph","created_at":"2026-05-18T01:04:49Z","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":"In this paper we generalize Tannakian formalism to fiber functors over general tensor categories. We will show that (under some technical conditions) if the fiber functor has a section, then the source category is equivalent to the category of comodules over a Hopf algebra in the target category. We will also give a description of this Hopf algebra using the notion of framed objects.","authors_text":"Amir Jafari, Mostafa Einollahzadeh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-09-10T10:15:15Z","title":"Tannakian formalism for fiber functors over tensor categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03023","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:be6ef87649de0bb715e4c3c8a4202d78d28bc4eb5551e283c541112dc741df00","target":"record","created_at":"2026-05-18T01:04:49Z","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":"2dc7c1f01cd569503671284486108bd3cf3bf5ce193fcf75da644f214c9fd28f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-09-10T10:15:15Z","title_canon_sha256":"4fa4005e683b32e30c4a83f417a61e544c6b3f05254c343ceb42dbd01aed683e"},"schema_version":"1.0","source":{"id":"1609.03023","kind":"arxiv","version":1}},"canonical_sha256":"ef7229bd66deee3b46516afec76d931d9c7867b9a9e12c2a1d68cf4cced04304","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef7229bd66deee3b46516afec76d931d9c7867b9a9e12c2a1d68cf4cced04304","first_computed_at":"2026-05-18T01:04:49.121518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:49.121518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Dr98xbRfGQa60fv9ilB6SHtFiGRkgCY0YIItM3UehoRCDyUg5oiRHM3q64KEoT7SwcfasGf65tTaTe+HWHGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:49.121937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03023","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be6ef87649de0bb715e4c3c8a4202d78d28bc4eb5551e283c541112dc741df00","sha256:5f1c91cc8fc096999652252170095fbf556821cb2fe0d236a7b3205f741f985b"],"state_sha256":"1a66c0583281d948348d403308b86e5951d0ece33a3196688f5847b8b175084c"}