{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PXFT7FNHZERPJ6G7YTR7WH65RX","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":"138302c0d6117384460002445efe19969a4f3935accde8aedf065d74cde2bfc2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-10-11T16:25:17Z","title_canon_sha256":"e2c2461c4c04d4a1f8f3b19f360aaea53dd94716d712f9b08c19ff80c7b5856e"},"schema_version":"1.0","source":{"id":"1710.04153","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04153","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04153v5","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04153","created_at":"2026-05-17T23:49:57Z"},{"alias_kind":"pith_short_12","alias_value":"PXFT7FNHZERP","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PXFT7FNHZERPJ6G7","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PXFT7FNH","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:019553eb98ca8f01bc23be2cfd660060b0b5f1689958e2ece4281b603d435808","target":"graph","created_at":"2026-05-17T23:49:57Z","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":"Let $R$ be an associative ring with unit. This paper deals with various aspects of the category of functors of $\\mathcal R$-modules; that is, the category of additive and covariant functors from the category of R-modules to the category of abelian groups. We give several characterizations of left-exact Mittag-Leffler functors of $\\mathcal R$-modules.","authors_text":"Adri\\'an Gordillo, Jos\\'e Navarro, Pedro Sancho","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-10-11T16:25:17Z","title":"Left-exact Mittag-Leffler functors of modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04153","kind":"arxiv","version":5},"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":"sha256:7bc208163c9c8ef30c8138ee93bce207820816399897afd6aab10a060b393803","target":"record","created_at":"2026-05-17T23:49:57Z","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":"138302c0d6117384460002445efe19969a4f3935accde8aedf065d74cde2bfc2","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-10-11T16:25:17Z","title_canon_sha256":"e2c2461c4c04d4a1f8f3b19f360aaea53dd94716d712f9b08c19ff80c7b5856e"},"schema_version":"1.0","source":{"id":"1710.04153","kind":"arxiv","version":5}},"canonical_sha256":"7dcb3f95a7c922f4f8dfc4e3fb1fdd8dd15206ceaeeceafc367f7cb29a982176","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dcb3f95a7c922f4f8dfc4e3fb1fdd8dd15206ceaeeceafc367f7cb29a982176","first_computed_at":"2026-05-17T23:49:57.524986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:57.524986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AwlFOpSO4hG5ORnjbKnf8sx5Y/tGtjL5+++xm9D1geKGOHNerMdaolJ56WMfgqcRcZufdTTTMS79alYqCnPOCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:57.525539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.04153","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bc208163c9c8ef30c8138ee93bce207820816399897afd6aab10a060b393803","sha256:019553eb98ca8f01bc23be2cfd660060b0b5f1689958e2ece4281b603d435808"],"state_sha256":"ddde6519c5d43f03cc406eb2b583ed75ceedf2f132baf6c10fd53d70fcafc138"}