{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SI6ZNV24VVLLELQJRZFIBATF3I","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":"edf7b2ad5e4dcdb77c5dbe69324c5bb3a33d7e744d588688bccdad221943fc6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-08T17:27:41Z","title_canon_sha256":"46ab8890fee70ddb1bd3033c00184233c0694d06e39c64422411a02db7edb194"},"schema_version":"1.0","source":{"id":"1111.1981","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1981","created_at":"2026-05-18T01:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1981v4","created_at":"2026-05-18T01:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1981","created_at":"2026-05-18T01:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"SI6ZNV24VVLL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SI6ZNV24VVLLELQJ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SI6ZNV24","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:fa5263b7d8d29d4e6110b237a57b4837ed68b1c40d4b37edb20e4ba9164d6bb5","target":"graph","created_at":"2026-05-18T01:35:52Z","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 study fiber functors on Tannakian categories which are equipped with a grading or a filtration. Our goal is to give a comprehensive set of foundational results about such functors. A main result is that each filtration on a fiber functor can be split by a grading fpqc-locally on the base scheme.","authors_text":"Paul Ziegler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-08T17:27:41Z","title":"Graded and Filtered Fiber Functors on Tannakian Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1981","kind":"arxiv","version":4},"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":"sha256:5bd35c5a4464b30d2517cce381562533548c4658f3795f7d934e8ce687864baa","target":"record","created_at":"2026-05-18T01:35:52Z","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":"edf7b2ad5e4dcdb77c5dbe69324c5bb3a33d7e744d588688bccdad221943fc6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-08T17:27:41Z","title_canon_sha256":"46ab8890fee70ddb1bd3033c00184233c0694d06e39c64422411a02db7edb194"},"schema_version":"1.0","source":{"id":"1111.1981","kind":"arxiv","version":4}},"canonical_sha256":"923d96d75cad56b22e098e4a808265da203966b649c1787cc7ddd4ee9ce597ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"923d96d75cad56b22e098e4a808265da203966b649c1787cc7ddd4ee9ce597ea","first_computed_at":"2026-05-18T01:35:52.614662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:52.614662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+pngS9cE4WHnvxeSb6eTDzNWQ7KlWqj0O+d40OhNkfrqaWoeSbZhfpdAZVAcOhrSZYWB4LIe10bhADC1jHYvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:52.615200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1981","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bd35c5a4464b30d2517cce381562533548c4658f3795f7d934e8ce687864baa","sha256:fa5263b7d8d29d4e6110b237a57b4837ed68b1c40d4b37edb20e4ba9164d6bb5"],"state_sha256":"3049fcc6d8d3d00a203bfadd7036987a49c9e73a25cf4549543932ebebe874cd"}