{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:45IEHG34WCGCT5ZXK33SP2LNCC","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":"9a16c426dbbe10a0644c235fd02376726424c6eb9636e2f338453493d233bf4f","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-20T20:55:16Z","title_canon_sha256":"07ab517d37e76f1d4bf5a23f8794678ba12e6b262b1edbd57539e37fc3f039fb"},"schema_version":"1.0","source":{"id":"2411.13706","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13706","created_at":"2026-07-05T09:38:36Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13706v1","created_at":"2026-07-05T09:38:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13706","created_at":"2026-07-05T09:38:36Z"},{"alias_kind":"pith_short_12","alias_value":"45IEHG34WCGC","created_at":"2026-07-05T09:38:36Z"},{"alias_kind":"pith_short_16","alias_value":"45IEHG34WCGCT5ZX","created_at":"2026-07-05T09:38:36Z"},{"alias_kind":"pith_short_8","alias_value":"45IEHG34","created_at":"2026-07-05T09:38:36Z"}],"graph_snapshots":[{"event_id":"sha256:27443dbe10722e221e09ab18dbf7b03633fdb7ce7b32ca8c271c04fd9d8fb949","target":"graph","created_at":"2026-07-05T09:38:36Z","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/2411.13706/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the spectrum of closed subcategories in a quasi-scheme, i.e. a Grothendieck category $X$. The closed subcategories are the direct analogs of closed subschemes in the commutative case, in the sense that when $X$ is the category of quasi-coherent sheaves on a quasi-projective scheme $S$, then the closed subschemes of $S$ correspond bijectively to the closed subcategories of $X$. Many interesting quasi-schemes, such as the noncommutative projective scheme Qgr-$B$ = Gr-$B$/Tors-$B$ associated to a graded algebra $B$, arise as quotient categories of simpler abelian categories. In this pape","authors_text":"Daniel Rogalski","cross_cats":["math.CT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-20T20:55:16Z","title":"Closed subcategories of quotient categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13706","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:fd2cb7aa715c6afd19a938a3ad099476e9bb8352a9de7044df382df04918d43b","target":"record","created_at":"2026-07-05T09:38:36Z","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":"9a16c426dbbe10a0644c235fd02376726424c6eb9636e2f338453493d233bf4f","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-11-20T20:55:16Z","title_canon_sha256":"07ab517d37e76f1d4bf5a23f8794678ba12e6b262b1edbd57539e37fc3f039fb"},"schema_version":"1.0","source":{"id":"2411.13706","kind":"arxiv","version":1}},"canonical_sha256":"e750439b7cb08c29f73756f727e96d108e5b45593362395627cef844535d2ccc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e750439b7cb08c29f73756f727e96d108e5b45593362395627cef844535d2ccc","first_computed_at":"2026-07-05T09:38:36.072396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:36.072396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Pv4MtHLmjwZPu9hQZp8A2ua1TdV/fzvFjX79rCPWB3p/RhxHZ2iEQn8WOWONq/Zrt6V17QGOmP/6CLW7BLRCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:36.072862Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13706","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd2cb7aa715c6afd19a938a3ad099476e9bb8352a9de7044df382df04918d43b","sha256:27443dbe10722e221e09ab18dbf7b03633fdb7ce7b32ca8c271c04fd9d8fb949"],"state_sha256":"78d25ce35ba93326258b5a2f238c35b947454e35cb0cf11e535150c4e30da73f"}