{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SVNFREZD3FEGDWLW6MGAL2P3EA","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":"369c49ce75026f51e3d0fba8aa607830d030c1e653f58e6f83c4a275b701d8d4","cross_cats_sorted":["math.RA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-11-25T11:56:44Z","title_canon_sha256":"f4ce08d09b1d1843930df26ec5b85e77ea30e6300ed895dd7277e14f75fa5216"},"schema_version":"1.0","source":{"id":"2411.16309","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16309","created_at":"2026-07-05T09:46:54Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16309v2","created_at":"2026-07-05T09:46:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16309","created_at":"2026-07-05T09:46:54Z"},{"alias_kind":"pith_short_12","alias_value":"SVNFREZD3FEG","created_at":"2026-07-05T09:46:54Z"},{"alias_kind":"pith_short_16","alias_value":"SVNFREZD3FEGDWLW","created_at":"2026-07-05T09:46:54Z"},{"alias_kind":"pith_short_8","alias_value":"SVNFREZD","created_at":"2026-07-05T09:46:54Z"}],"graph_snapshots":[{"event_id":"sha256:675da688c242e0f0da74e0d9f43a8f3cf9cc0a8b2955ae56232e1a30b5dca28a","target":"graph","created_at":"2026-07-05T09:46:54Z","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/2411.16309/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A notion of support for objects in any Grothendieck category is introduced. This is based on the spectral category of a Grothendieck category and uses its Boolean lattice of localising subcategories. The support provides a classification of all subcategories that are closed under arbitrary coproducts, subobjects, and essential extensions. There is also a notion of exact support which classifies certain thick subcategories. As an application, the coproduct decompositions of objects are described in terms of Boolean lattices. Also, for any ring Crawley-Boevey's correspondence between definable s","authors_text":"Henning Krause","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-11-25T11:56:44Z","title":"The Boolean spectrum of a Grothendieck category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16309","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:a5c959dcb6b235a4229a35361a23f064fdbb76ee34d41d205819a9e685c18c6a","target":"record","created_at":"2026-07-05T09:46:54Z","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":"369c49ce75026f51e3d0fba8aa607830d030c1e653f58e6f83c4a275b701d8d4","cross_cats_sorted":["math.RA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-11-25T11:56:44Z","title_canon_sha256":"f4ce08d09b1d1843930df26ec5b85e77ea30e6300ed895dd7277e14f75fa5216"},"schema_version":"1.0","source":{"id":"2411.16309","kind":"arxiv","version":2}},"canonical_sha256":"955a589323d94861d976f30c05e9fb200012e7cb42ba9cb8ad5fb0d287bc205f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"955a589323d94861d976f30c05e9fb200012e7cb42ba9cb8ad5fb0d287bc205f","first_computed_at":"2026-07-05T09:46:54.974126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:46:54.974126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cCHVloEyQgNBV0PRbTwS64n0bUutM2tJLAZewc3eJJ1qkuBpOP170nWXicknhgUzaTTLTuON3AdkpjjZKSwwBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:46:54.974677Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16309","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5c959dcb6b235a4229a35361a23f064fdbb76ee34d41d205819a9e685c18c6a","sha256:675da688c242e0f0da74e0d9f43a8f3cf9cc0a8b2955ae56232e1a30b5dca28a"],"state_sha256":"e3e6285127a7da9223e8ab96b6bdec996bc515d2bcfdabf1f7ebc14b2f657acc"}