{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VLEAEDASVQQ7KJAUPX62RCQMWU","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":"d8623ce155298095726849e6ab324c2d1fe7eb570349a0acb5ad161a12fb6b14","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-08T12:17:54Z","title_canon_sha256":"8061d64e8be6037749ebfb595527ad043a684b62b48774b908247b798dc4a71a"},"schema_version":"1.0","source":{"id":"2606.09398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09398","created_at":"2026-06-09T02:08:20Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09398v1","created_at":"2026-06-09T02:08:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09398","created_at":"2026-06-09T02:08:20Z"},{"alias_kind":"pith_short_12","alias_value":"VLEAEDASVQQ7","created_at":"2026-06-09T02:08:20Z"},{"alias_kind":"pith_short_16","alias_value":"VLEAEDASVQQ7KJAU","created_at":"2026-06-09T02:08:20Z"},{"alias_kind":"pith_short_8","alias_value":"VLEAEDAS","created_at":"2026-06-09T02:08:20Z"}],"graph_snapshots":[{"event_id":"sha256:ce0d356adb078d54cbfe71325d8cf1ebacf4e3e6b1a9b62204d561eb4eaf4f57","target":"graph","created_at":"2026-06-09T02:08:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.09398/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $A$ be a bounded non positive commutative differential graded algebra $A$. Let $\\mathbf{D}(A)$ its derived category of DG-modules. If $\\mathbf{D}(A)$ is generated by the DG-modules corresponding to the residue fields of the ordinary ring $H^0(A)$ then its localizing subcategories and its colocalizing subcategories are in bijection with the subsets of $\\textrm{Spec}(H^0(A))$. These results generalize well-known theorems by A. Neeman (from 1992 and 2011, respectively), because any Noetherian ring satisfies this condition.","authors_text":"Ana Jerem\\'ias, Eduardo Loureiro, Leovigildo Alonso","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-08T12:17:54Z","title":"Colocalizing subcategories on differentially graded algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09398","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:c0cd5ece83b9722536961e415d06d2f51c71962ed5cfd838f5a75993b0f823c4","target":"record","created_at":"2026-06-09T02:08:20Z","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":"d8623ce155298095726849e6ab324c2d1fe7eb570349a0acb5ad161a12fb6b14","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-08T12:17:54Z","title_canon_sha256":"8061d64e8be6037749ebfb595527ad043a684b62b48774b908247b798dc4a71a"},"schema_version":"1.0","source":{"id":"2606.09398","kind":"arxiv","version":1}},"canonical_sha256":"aac8020c12ac21f524147dfda88a0cb511c5ab272b74a847c9ea4c3a2f9ffbdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aac8020c12ac21f524147dfda88a0cb511c5ab272b74a847c9ea4c3a2f9ffbdb","first_computed_at":"2026-06-09T02:08:20.044718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:20.044718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HhApWM2oKup7WDTpN4aLVCVCDPBcuX1EpgOr0wkXTqwRgXq61zM8cPnR/waV0ogPd+571uGkSlTZsQjIBUD1BA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:20.045600Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0cd5ece83b9722536961e415d06d2f51c71962ed5cfd838f5a75993b0f823c4","sha256:ce0d356adb078d54cbfe71325d8cf1ebacf4e3e6b1a9b62204d561eb4eaf4f57"],"state_sha256":"bddcbe9e5a3a07884162d06964ef289ae3545223095495f79a821dc1c9fcbf86"}