{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GR4HDUYNRY5MMEVB37NS4GBCHJ","short_pith_number":"pith:GR4HDUYN","schema_version":"1.0","canonical_sha256":"347871d30d8e3ac612a1dfdb2e18223a74dd304213ede1510e255bb511d89fe3","source":{"kind":"arxiv","id":"2502.21064","version":3},"attestation_state":"computed","paper":{"title":"Higher extension closure and $d$-exact categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Sondre Kvamme","submitted_at":"2025-02-28T14:01:06Z","abstract_excerpt":"We prove that any weakly idempotent complete $d$-exact category is equivalent to a $d$-cluster tilting subcategory of a weakly idempotent complete exact category, and that any weakly idempotent complete algebraic $(d+2)$-angulated category is equivalent to a $d$-cluster tilting subcategory of an algebraic triangulated category closed under $d$-shifts. Furthermore, we show that the ambient exact category of a $d$-cluster tilting subcategory is unique up to exact equivalence, assuming it is weakly idempotent complete. This follows from the inclusion of the $d$-cluster tilting subcategory satisfy"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2502.21064","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-02-28T14:01:06Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"a4b3dbbc09ed829bf8d46da7333a698c2aa2384bb3be2b075bb0205f79e14ca6","abstract_canon_sha256":"ea1c5c31d044a2282ae29b791827d74330c8f1d2c028bbbb0a6be0a7bf23a281"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:11.329473Z","signature_b64":"YbgynjRTlzUcj93SWWHwi2TKJJ3Lvc5GbspRwsKu/L8gJAPi5solRsxfPdqeEOHGD1meQwaNCyuwNnhSrfO+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"347871d30d8e3ac612a1dfdb2e18223a74dd304213ede1510e255bb511d89fe3","last_reissued_at":"2026-05-26T01:03:11.328570Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:11.328570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher extension closure and $d$-exact categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Sondre Kvamme","submitted_at":"2025-02-28T14:01:06Z","abstract_excerpt":"We prove that any weakly idempotent complete $d$-exact category is equivalent to a $d$-cluster tilting subcategory of a weakly idempotent complete exact category, and that any weakly idempotent complete algebraic $(d+2)$-angulated category is equivalent to a $d$-cluster tilting subcategory of an algebraic triangulated category closed under $d$-shifts. Furthermore, we show that the ambient exact category of a $d$-cluster tilting subcategory is unique up to exact equivalence, assuming it is weakly idempotent complete. This follows from the inclusion of the $d$-cluster tilting subcategory satisfy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.21064","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.21064/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2502.21064","created_at":"2026-05-26T01:03:11.328698+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.21064v3","created_at":"2026-05-26T01:03:11.328698+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.21064","created_at":"2026-05-26T01:03:11.328698+00:00"},{"alias_kind":"pith_short_12","alias_value":"GR4HDUYNRY5M","created_at":"2026-05-26T01:03:11.328698+00:00"},{"alias_kind":"pith_short_16","alias_value":"GR4HDUYNRY5MMEVB","created_at":"2026-05-26T01:03:11.328698+00:00"},{"alias_kind":"pith_short_8","alias_value":"GR4HDUYN","created_at":"2026-05-26T01:03:11.328698+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ","json":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ.json","graph_json":"https://pith.science/api/pith-number/GR4HDUYNRY5MMEVB37NS4GBCHJ/graph.json","events_json":"https://pith.science/api/pith-number/GR4HDUYNRY5MMEVB37NS4GBCHJ/events.json","paper":"https://pith.science/paper/GR4HDUYN"},"agent_actions":{"view_html":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ","download_json":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ.json","view_paper":"https://pith.science/paper/GR4HDUYN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.21064&json=true","fetch_graph":"https://pith.science/api/pith-number/GR4HDUYNRY5MMEVB37NS4GBCHJ/graph.json","fetch_events":"https://pith.science/api/pith-number/GR4HDUYNRY5MMEVB37NS4GBCHJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ/action/storage_attestation","attest_author":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ/action/author_attestation","sign_citation":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ/action/citation_signature","submit_replication":"https://pith.science/pith/GR4HDUYNRY5MMEVB37NS4GBCHJ/action/replication_record"}},"created_at":"2026-05-26T01:03:11.328698+00:00","updated_at":"2026-05-26T01:03:11.328698+00:00"}