{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KOZHHSKVIASCLY43DEJXNIFNNS","short_pith_number":"pith:KOZHHSKV","canonical_record":{"source":{"id":"1510.04885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-10-16T13:51:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b144d13d5705e6b5ea9226244b0216dc93bddbe6d7a60346d058092b68bf0f6d","abstract_canon_sha256":"f2374e5e644dab6e86482e1626f04636d1d12c3debc9bb5e175f9da3d6c89077"},"schema_version":"1.0"},"canonical_sha256":"53b273c955402425e39b191376a0ad6c9f90a25bb1bf59866727f000cb011314","source":{"kind":"arxiv","id":"1510.04885","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04885","created_at":"2026-05-18T01:30:00Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04885v1","created_at":"2026-05-18T01:30:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04885","created_at":"2026-05-18T01:30:00Z"},{"alias_kind":"pith_short_12","alias_value":"KOZHHSKVIASC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KOZHHSKVIASCLY43","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KOZHHSKV","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KOZHHSKVIASCLY43DEJXNIFNNS","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-10-16T13:51:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b144d13d5705e6b5ea9226244b0216dc93bddbe6d7a60346d058092b68bf0f6d","abstract_canon_sha256":"f2374e5e644dab6e86482e1626f04636d1d12c3debc9bb5e175f9da3d6c89077"},"schema_version":"1.0"},"canonical_sha256":"53b273c955402425e39b191376a0ad6c9f90a25bb1bf59866727f000cb011314","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:00.374584Z","signature_b64":"e6/FmxBOq8A9ZOuvy8mtDhAq4uWxiokMtDePdrXweIMlDTzoMxIp7a0MeQ+QiINAVgrYQVQ/aMnqcCNDeI4gDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53b273c955402425e39b191376a0ad6c9f90a25bb1bf59866727f000cb011314","last_reissued_at":"2026-05-18T01:30:00.373886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:00.373886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04885","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PibsQ92SiJWc6+rQaX4KIZyPHNCOpOb7FSIfhZPr+j8nKWLdS5p3jmelbnmhVaIUMmjHj+qbUdMRxayug9M7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:43:37.962626Z"},"content_sha256":"2da8c02f2f00f0385ba7340fd9c5be47f0852c70f02775d884844511aefeebe5","schema_version":"1.0","event_id":"sha256:2da8c02f2f00f0385ba7340fd9c5be47f0852c70f02775d884844511aefeebe5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KOZHHSKVIASCLY43DEJXNIFNNS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adjunctions of quasi-functors between dg-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CT","authors_text":"Francesco Genovese","submitted_at":"2015-10-16T13:51:26Z","abstract_excerpt":"We study right quasi-representable differential graded bimodules as quasi-functors between dg-categories. We prove that a quasi-functor has a left adjoint if and only if it is left quasi-representable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04885","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMzMP/RVkqOiUSGu+WyofwSS3gBTaBPs2Y3rJz5xeml3vzyrZOw2Rm96ZSwHLYmpDJUYEjeIqvlnptV2pLAtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:43:37.962961Z"},"content_sha256":"ee29bd8eb31000423fec2f077336224f6e648eec5596b3ed17a2476231a9bcb1","schema_version":"1.0","event_id":"sha256:ee29bd8eb31000423fec2f077336224f6e648eec5596b3ed17a2476231a9bcb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOZHHSKVIASCLY43DEJXNIFNNS/bundle.json","state_url":"https://pith.science/pith/KOZHHSKVIASCLY43DEJXNIFNNS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOZHHSKVIASCLY43DEJXNIFNNS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T10:43:37Z","links":{"resolver":"https://pith.science/pith/KOZHHSKVIASCLY43DEJXNIFNNS","bundle":"https://pith.science/pith/KOZHHSKVIASCLY43DEJXNIFNNS/bundle.json","state":"https://pith.science/pith/KOZHHSKVIASCLY43DEJXNIFNNS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOZHHSKVIASCLY43DEJXNIFNNS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KOZHHSKVIASCLY43DEJXNIFNNS","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":"f2374e5e644dab6e86482e1626f04636d1d12c3debc9bb5e175f9da3d6c89077","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-10-16T13:51:26Z","title_canon_sha256":"b144d13d5705e6b5ea9226244b0216dc93bddbe6d7a60346d058092b68bf0f6d"},"schema_version":"1.0","source":{"id":"1510.04885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04885","created_at":"2026-05-18T01:30:00Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04885v1","created_at":"2026-05-18T01:30:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04885","created_at":"2026-05-18T01:30:00Z"},{"alias_kind":"pith_short_12","alias_value":"KOZHHSKVIASC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KOZHHSKVIASCLY43","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KOZHHSKV","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:ee29bd8eb31000423fec2f077336224f6e648eec5596b3ed17a2476231a9bcb1","target":"graph","created_at":"2026-05-18T01:30:00Z","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"},"paper":{"abstract_excerpt":"We study right quasi-representable differential graded bimodules as quasi-functors between dg-categories. We prove that a quasi-functor has a left adjoint if and only if it is left quasi-representable.","authors_text":"Francesco Genovese","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-10-16T13:51:26Z","title":"Adjunctions of quasi-functors between dg-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04885","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":"sha256:2da8c02f2f00f0385ba7340fd9c5be47f0852c70f02775d884844511aefeebe5","target":"record","created_at":"2026-05-18T01:30:00Z","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":"f2374e5e644dab6e86482e1626f04636d1d12c3debc9bb5e175f9da3d6c89077","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-10-16T13:51:26Z","title_canon_sha256":"b144d13d5705e6b5ea9226244b0216dc93bddbe6d7a60346d058092b68bf0f6d"},"schema_version":"1.0","source":{"id":"1510.04885","kind":"arxiv","version":1}},"canonical_sha256":"53b273c955402425e39b191376a0ad6c9f90a25bb1bf59866727f000cb011314","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53b273c955402425e39b191376a0ad6c9f90a25bb1bf59866727f000cb011314","first_computed_at":"2026-05-18T01:30:00.373886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:00.373886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e6/FmxBOq8A9ZOuvy8mtDhAq4uWxiokMtDePdrXweIMlDTzoMxIp7a0MeQ+QiINAVgrYQVQ/aMnqcCNDeI4gDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:00.374584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2da8c02f2f00f0385ba7340fd9c5be47f0852c70f02775d884844511aefeebe5","sha256:ee29bd8eb31000423fec2f077336224f6e648eec5596b3ed17a2476231a9bcb1"],"state_sha256":"fa1510b7f24f7f0de0e37f0c6d3c6a02f16220691e2265d7aed65426d682ce17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"50ot2gknGYq5v+ArnU116K7HViRMst64rftJBW5V+gpT6YiUHQg8T59LfoCqoWxH0cqWPCuUZsu4lJkikEHUAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T10:43:37.964755Z","bundle_sha256":"044215c84b9e45d2b79d07ff761f878cda3b62f43b28f64469b75d617e905854"}}