{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YHEKJJTG4EFSBU6N7MMMZTK2MC","short_pith_number":"pith:YHEKJJTG","canonical_record":{"source":{"id":"1805.03485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-09T12:45:25Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"362e1ca5d6b58986224e996f9877de8934b036d0a0a4d21721aeb87f99e4e95b","abstract_canon_sha256":"24f78b32a3552e3c0cb08ef682cf8285267b375be37588f02f8fc65169b63200"},"schema_version":"1.0"},"canonical_sha256":"c1c8a4a666e10b20d3cdfb18cccd5a60adb8af751d01586aaccd9a6281e2feca","source":{"kind":"arxiv","id":"1805.03485","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03485","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03485v1","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03485","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"YHEKJJTG4EFS","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YHEKJJTG4EFSBU6N","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YHEKJJTG","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YHEKJJTG4EFSBU6N7MMMZTK2MC","target":"record","payload":{"canonical_record":{"source":{"id":"1805.03485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-09T12:45:25Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"362e1ca5d6b58986224e996f9877de8934b036d0a0a4d21721aeb87f99e4e95b","abstract_canon_sha256":"24f78b32a3552e3c0cb08ef682cf8285267b375be37588f02f8fc65169b63200"},"schema_version":"1.0"},"canonical_sha256":"c1c8a4a666e10b20d3cdfb18cccd5a60adb8af751d01586aaccd9a6281e2feca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:20.103193Z","signature_b64":"UehI7j805bUE3fLA62wDMSDwz4HFu7+mlo0fGQ7uPA4Zd0N2+rqfVZ/VgiyncfXajaxIpd9ohePJVVV6vEhcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1c8a4a666e10b20d3cdfb18cccd5a60adb8af751d01586aaccd9a6281e2feca","last_reissued_at":"2026-05-18T00:16:20.102723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:20.102723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.03485","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":"2026-05-18T00:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6NBfDxJLbrI6MI130xc6oLZCtbCpVZML3sEAfwSEWITSaON6Zn/9Ix5ImUaUKqhnOzg9vM5XUVPRuocb90oDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:06:06.745354Z"},"content_sha256":"2b31a24fa11f3365e8f953bfdd8878d61994aa916d239ce4764469ef2286984f","schema_version":"1.0","event_id":"sha256:2b31a24fa11f3365e8f953bfdd8878d61994aa916d239ce4764469ef2286984f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YHEKJJTG4EFSBU6N7MMMZTK2MC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of fiber functors and universal Tannakian categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Daniel Sch\\\"appi","submitted_at":"2018-05-09T12:45:25Z","abstract_excerpt":"The principal aim of this note is to give an elementary proof of the fact that any two fiber functors of a Tannakian category are locally isomorphic. This builds on an idea of Deligne concerning scalar extensions of Tannakian categories and implements a proof strategy which Deligne attributes to Grothendieck. Besides categorical generalities, the proof merely relies on basic properties of exterior powers and the classification of finitely generated modules over a principal ideal domain.\n  Using related ideas (but less elementary means) we also present an alternative characterization of Tannaki"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03485","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":"2026-05-18T00:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfgtoLSWdiAsingoiQB1ep8VqHIiHcXMNLAGTkzZwDlrFhZ0sT8kkhSjt72uW7CO0BhGQVJ5fmih/f3bRCzRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:06:06.746299Z"},"content_sha256":"7789c21638b6bd339496fb7240abc065ece2ebf029e1b592df3905e120ee66cf","schema_version":"1.0","event_id":"sha256:7789c21638b6bd339496fb7240abc065ece2ebf029e1b592df3905e120ee66cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YHEKJJTG4EFSBU6N7MMMZTK2MC/bundle.json","state_url":"https://pith.science/pith/YHEKJJTG4EFSBU6N7MMMZTK2MC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YHEKJJTG4EFSBU6N7MMMZTK2MC/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":"2026-08-09T09:06:06Z","links":{"resolver":"https://pith.science/pith/YHEKJJTG4EFSBU6N7MMMZTK2MC","bundle":"https://pith.science/pith/YHEKJJTG4EFSBU6N7MMMZTK2MC/bundle.json","state":"https://pith.science/pith/YHEKJJTG4EFSBU6N7MMMZTK2MC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YHEKJJTG4EFSBU6N7MMMZTK2MC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YHEKJJTG4EFSBU6N7MMMZTK2MC","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":"24f78b32a3552e3c0cb08ef682cf8285267b375be37588f02f8fc65169b63200","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-09T12:45:25Z","title_canon_sha256":"362e1ca5d6b58986224e996f9877de8934b036d0a0a4d21721aeb87f99e4e95b"},"schema_version":"1.0","source":{"id":"1805.03485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03485","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03485v1","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03485","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"YHEKJJTG4EFS","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YHEKJJTG4EFSBU6N","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YHEKJJTG","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:7789c21638b6bd339496fb7240abc065ece2ebf029e1b592df3905e120ee66cf","target":"graph","created_at":"2026-05-18T00:16:20Z","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":"The principal aim of this note is to give an elementary proof of the fact that any two fiber functors of a Tannakian category are locally isomorphic. This builds on an idea of Deligne concerning scalar extensions of Tannakian categories and implements a proof strategy which Deligne attributes to Grothendieck. Besides categorical generalities, the proof merely relies on basic properties of exterior powers and the classification of finitely generated modules over a principal ideal domain.\n  Using related ideas (but less elementary means) we also present an alternative characterization of Tannaki","authors_text":"Daniel Sch\\\"appi","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-09T12:45:25Z","title":"Uniqueness of fiber functors and universal Tannakian categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03485","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":"sha256:2b31a24fa11f3365e8f953bfdd8878d61994aa916d239ce4764469ef2286984f","target":"record","created_at":"2026-05-18T00:16:20Z","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":"24f78b32a3552e3c0cb08ef682cf8285267b375be37588f02f8fc65169b63200","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-05-09T12:45:25Z","title_canon_sha256":"362e1ca5d6b58986224e996f9877de8934b036d0a0a4d21721aeb87f99e4e95b"},"schema_version":"1.0","source":{"id":"1805.03485","kind":"arxiv","version":1}},"canonical_sha256":"c1c8a4a666e10b20d3cdfb18cccd5a60adb8af751d01586aaccd9a6281e2feca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1c8a4a666e10b20d3cdfb18cccd5a60adb8af751d01586aaccd9a6281e2feca","first_computed_at":"2026-05-18T00:16:20.102723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:20.102723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UehI7j805bUE3fLA62wDMSDwz4HFu7+mlo0fGQ7uPA4Zd0N2+rqfVZ/VgiyncfXajaxIpd9ohePJVVV6vEhcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:20.103193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b31a24fa11f3365e8f953bfdd8878d61994aa916d239ce4764469ef2286984f","sha256:7789c21638b6bd339496fb7240abc065ece2ebf029e1b592df3905e120ee66cf"],"state_sha256":"dd896fc42edd1e8306399e5f77d2731de20d6c56b95345dab316d3b490bbceeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aecicz8/1QeZqhDdx+TyMccAJUVn4v3HDaOeWtqCeWJrzDh2XYSveWUptSUll/c8WieRRVZVvvd1GDnoTvQqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:06:06.750836Z","bundle_sha256":"3d9a0f0ac38a0b19e906d99ba1ce2dff7421199632e5d80ca55edee9f60debb5"}}