{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RC6XWWCEQZLEO2CG22GFLW5YWI","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":"c1e6420da0064dd654752599f7e129a7de991fcb5c1e7a9d4b994a375d12b650","cross_cats_sorted":["math.AG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-04-09T20:40:49Z","title_canon_sha256":"588b5882f43579d668ef4b68469215623e9ea0dffc53ba067ca72d1ba1067fb8"},"schema_version":"1.0","source":{"id":"2404.06610","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06610","created_at":"2026-07-05T09:21:26Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06610v3","created_at":"2026-07-05T09:21:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06610","created_at":"2026-07-05T09:21:26Z"},{"alias_kind":"pith_short_12","alias_value":"RC6XWWCEQZLE","created_at":"2026-07-05T09:21:26Z"},{"alias_kind":"pith_short_16","alias_value":"RC6XWWCEQZLEO2CG","created_at":"2026-07-05T09:21:26Z"},{"alias_kind":"pith_short_8","alias_value":"RC6XWWCE","created_at":"2026-07-05T09:21:26Z"}],"graph_snapshots":[{"event_id":"sha256:b384014d363bed4499b854516727b10adea94cf8de4567b2b18fccb3a221b6ea","target":"graph","created_at":"2026-07-05T09:21:26Z","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/2404.06610/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that, over an arbitrary commutative ring, the localizations of the categories of dg categories, of cohomologically unital, of unital and of strictly unital $A_\\infty$ categories with respect to the corresponding classes of quasi-equivalences are all equivalent. The result is proven at the $\\infty$-categorical level by considering the natural $\\infty$-categorical models of the categories above. As an application of the techniques we develop to compare the localizations mentioned above, we provide a new proof of the existence of internal Homs for the homotopy category of dg categories in","authors_text":"Alberto Canonaco, Mattia Ornaghi, Paolo Stellari","cross_cats":["math.AG","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-04-09T20:40:49Z","title":"Localizations of the categories of $A_\\infty$ categories and internal Homs over a ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06610","kind":"arxiv","version":3},"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":"sha256:2ea074455457ed79c795aa750bedbb66f812a34e5b55c6d05878cbd51c0c8fb0","target":"record","created_at":"2026-07-05T09:21:26Z","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":"c1e6420da0064dd654752599f7e129a7de991fcb5c1e7a9d4b994a375d12b650","cross_cats_sorted":["math.AG","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-04-09T20:40:49Z","title_canon_sha256":"588b5882f43579d668ef4b68469215623e9ea0dffc53ba067ca72d1ba1067fb8"},"schema_version":"1.0","source":{"id":"2404.06610","kind":"arxiv","version":3}},"canonical_sha256":"88bd7b58448656476846d68c55dbb8b21f5eb525d4e3825592af66a666a445b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88bd7b58448656476846d68c55dbb8b21f5eb525d4e3825592af66a666a445b1","first_computed_at":"2026-07-05T09:21:26.238196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:21:26.238196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d80/CavTIHqsmIhAZVOa8CohtdhN6G4gJ2JZ+mtOKrDnSid/3s/WEYRlDH6bnxN7fp44lbanC9Qv9HmItS0CCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:21:26.238692Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.06610","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ea074455457ed79c795aa750bedbb66f812a34e5b55c6d05878cbd51c0c8fb0","sha256:b384014d363bed4499b854516727b10adea94cf8de4567b2b18fccb3a221b6ea"],"state_sha256":"dbc2e9b6626f13c5775c7a12b98f46ff2f7dcdc7610c1a9b684e2c943f73a73e"}