{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:QEMUZEQ744ZHIA7LZVSP7CZSDH","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":"c76c6b9f3baea3732cb9912e3fdfe3d5e0848e8306560e145f1191242a474b09","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-09-21T17:00:01Z","title_canon_sha256":"ef1e28a1c28a1365ed7fb6e0180fe250971a5f5497d68d536355f62007e52965"},"schema_version":"1.0","source":{"id":"2009.10024","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.10024","created_at":"2026-07-05T06:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"2009.10024v4","created_at":"2026-07-05T06:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.10024","created_at":"2026-07-05T06:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"QEMUZEQ744ZH","created_at":"2026-07-05T06:31:55Z"},{"alias_kind":"pith_short_16","alias_value":"QEMUZEQ744ZHIA7L","created_at":"2026-07-05T06:31:55Z"},{"alias_kind":"pith_short_8","alias_value":"QEMUZEQ7","created_at":"2026-07-05T06:31:55Z"}],"graph_snapshots":[{"event_id":"sha256:707fc4768c70733201a5df55265802477ea00a3651fc4c479f864313a4b7d72a","target":"graph","created_at":"2026-07-05T06:31:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.10024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We initiate in this article the study of weakly exact structures, a generalization of Quillen exact structures. We introduce weak counterparts of one-sided exact structures and show that a left and a right weakly exact structure generate a weakly exact structure. We further define weakly extriangulated structures on an additive category $\\mathcal{A}$ and characterize weakly exact structures among them.\n  We investigate when these structures on $\\mathcal{A}$ form lattices. We prove that the lattice of substructures of a weakly extriangulated structure is isomorphic to the lattice of topologizin","authors_text":"Mikhail Gorsky, Rose-Line Baillargeon, Souheila Hassoun, Thomas Br\\\"ustle","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-09-21T17:00:01Z","title":"On the lattices of exact and weakly exact structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.10024","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":"sha256:355924254c831947a52d50247d39bc796ed867353949a6127b6e5434c25c3191","target":"record","created_at":"2026-07-05T06:31:55Z","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":"c76c6b9f3baea3732cb9912e3fdfe3d5e0848e8306560e145f1191242a474b09","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2020-09-21T17:00:01Z","title_canon_sha256":"ef1e28a1c28a1365ed7fb6e0180fe250971a5f5497d68d536355f62007e52965"},"schema_version":"1.0","source":{"id":"2009.10024","kind":"arxiv","version":4}},"canonical_sha256":"81194c921fe7327403ebcd64ff8b3219f4e69c34c6aee21e913e85415f5196e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81194c921fe7327403ebcd64ff8b3219f4e69c34c6aee21e913e85415f5196e9","first_computed_at":"2026-07-05T06:31:55.880440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:31:55.880440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PqIMLnDvitOHy3/AZ7qH2e2V5RYpbRAb1JRh5rBEMoeRvGncYNPoU6/AlXeveck0oSvMz/2PGcTvwomovePvAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:31:55.880845Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.10024","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:355924254c831947a52d50247d39bc796ed867353949a6127b6e5434c25c3191","sha256:707fc4768c70733201a5df55265802477ea00a3651fc4c479f864313a4b7d72a"],"state_sha256":"37274f825d9cc5b1eaaea5e4fa40dcd4f22da5f1ee4df8a1089b3ce557e9fc34"}