{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I7EX4T5HSBHHW56UA7X6PN45XB","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":"b0aa0db74316ba026a522a566d680657895c10873a192ed0c606a6809daa25b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-02-15T15:15:32Z","title_canon_sha256":"4fe71d44accfbc32394807a7b55834f1ab1862218d26ce332973c53b4fba19e6"},"schema_version":"1.0","source":{"id":"1202.3337","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3337","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3337v2","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3337","created_at":"2026-05-18T00:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"I7EX4T5HSBHH","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I7EX4T5HSBHHW56U","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I7EX4T5H","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:36a78957ca125ed8489695ae60ba339118570cd2431331c449a874224e63407d","target":"graph","created_at":"2026-05-18T00:55:58Z","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 define Gabriel monads as the idempotent monads associated to exact reflective localizations in Abelian categories and characterize them by a simple set of properties. The coimage of a Gabriel monad is a Serre quotient category. The Gabriel monad induces an equivalence between its coimage and its image, the localizing subcategory of local objects.","authors_text":"Markus Lange-Hegermann, Mohamed Barakat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-02-15T15:15:32Z","title":"On monads of exact reflective localizations of Abelian categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3337","kind":"arxiv","version":2},"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":"sha256:1b7526b06558db46bcd81bf854c4fac71e23024516efe8c04d8ecaf7037c15ee","target":"record","created_at":"2026-05-18T00:55:58Z","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":"b0aa0db74316ba026a522a566d680657895c10873a192ed0c606a6809daa25b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-02-15T15:15:32Z","title_canon_sha256":"4fe71d44accfbc32394807a7b55834f1ab1862218d26ce332973c53b4fba19e6"},"schema_version":"1.0","source":{"id":"1202.3337","kind":"arxiv","version":2}},"canonical_sha256":"47c97e4fa7904e7b77d407efe7b79db85262b897c802a70f70a9d81856b0d4ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47c97e4fa7904e7b77d407efe7b79db85262b897c802a70f70a9d81856b0d4ef","first_computed_at":"2026-05-18T00:55:58.896967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:58.896967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+0ohbe9D7IUqWufH0s9yEnCVMybAwMtkYgZdMmu4j7B9Qi76ptuqYD7WzUeKI3mH3El5AbmMtsfXYlu2cZqbAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:58.897587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3337","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b7526b06558db46bcd81bf854c4fac71e23024516efe8c04d8ecaf7037c15ee","sha256:36a78957ca125ed8489695ae60ba339118570cd2431331c449a874224e63407d"],"state_sha256":"ee9a5c639f60814dd9cc3c8d923c9f336932fe780f6e98cdfaa60f56f5251a9e"}