{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IIT3YL3CDGHYP6G2K4ELB4Z2IH","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":"d314496c6bd7272a969015cfc0037ef951cc43041cf0d6d9011cf729e4087eeb","cross_cats_sorted":["math.CT","math.LO","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2018-01-24T15:15:59Z","title_canon_sha256":"810eb6e984d96bc49485446ef1b4a361e9c864fe8be73a85cac58420a0080730"},"schema_version":"1.0","source":{"id":"1801.08015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08015","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08015v1","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08015","created_at":"2026-05-18T00:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"IIT3YL3CDGHY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IIT3YL3CDGHYP6G2","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IIT3YL3C","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:a851de5e2bcd12ae8965ddaad0d6503e968298a0ad8a8491ccdb6ee820135a27","target":"graph","created_at":"2026-05-18T00:25:10Z","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 can define a module to be an exact functor on a small abelian category. This is explained and shown to be equivalent to the usual definition but it does offer a different perspective, inspired by the notions from model theory of imaginary sort and interpretation. A number of examples are worked through.","authors_text":"Mike Prest","cross_cats":["math.CT","math.LO","math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2018-01-24T15:15:59Z","title":"Modules as exact functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08015","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:f8f80ca1be73c208e903710c122465a86fb377c517d476812f4f0dd965c294f3","target":"record","created_at":"2026-05-18T00:25:10Z","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":"d314496c6bd7272a969015cfc0037ef951cc43041cf0d6d9011cf729e4087eeb","cross_cats_sorted":["math.CT","math.LO","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2018-01-24T15:15:59Z","title_canon_sha256":"810eb6e984d96bc49485446ef1b4a361e9c864fe8be73a85cac58420a0080730"},"schema_version":"1.0","source":{"id":"1801.08015","kind":"arxiv","version":1}},"canonical_sha256":"4227bc2f62198f87f8da5708b0f33a41e43c1e855631301085131095e258a794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4227bc2f62198f87f8da5708b0f33a41e43c1e855631301085131095e258a794","first_computed_at":"2026-05-18T00:25:10.339404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:10.339404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/jbOhkdIPHjDJ1xvfunI5TxlNZp5eqixV1aE3FkLBilCL4zOLAwwWRPl0tE/18HRfD5DIJ4qQxLAzX4LBiECg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:10.339969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8f80ca1be73c208e903710c122465a86fb377c517d476812f4f0dd965c294f3","sha256:a851de5e2bcd12ae8965ddaad0d6503e968298a0ad8a8491ccdb6ee820135a27"],"state_sha256":"c4d488898fd609b970a75ed0ff7f3202fddce761ed7e3e9f7fef736da817a7b7"}