{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YHKD4J5RJFLNZSGS6B5QEYFQFA","short_pith_number":"pith:YHKD4J5R","canonical_record":{"source":{"id":"1310.8279","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-30T19:29:24Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"a06a685370739ebd46088a85b87f8b843864bfab20af4295f860deb5c5d525d8","abstract_canon_sha256":"e0a41e42d4348e5ac6b6690bd244e30d8c0b0661cd4b5ee692dc63d38fe8670a"},"schema_version":"1.0"},"canonical_sha256":"c1d43e27b14956dcc8d2f07b0260b0283694741c3c578aa3252460da23c7c238","source":{"kind":"arxiv","id":"1310.8279","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8279","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8279v4","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8279","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"YHKD4J5RJFLN","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YHKD4J5RJFLNZSGS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YHKD4J5R","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YHKD4J5RJFLNZSGS6B5QEYFQFA","target":"record","payload":{"canonical_record":{"source":{"id":"1310.8279","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-30T19:29:24Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"a06a685370739ebd46088a85b87f8b843864bfab20af4295f860deb5c5d525d8","abstract_canon_sha256":"e0a41e42d4348e5ac6b6690bd244e30d8c0b0661cd4b5ee692dc63d38fe8670a"},"schema_version":"1.0"},"canonical_sha256":"c1d43e27b14956dcc8d2f07b0260b0283694741c3c578aa3252460da23c7c238","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:26.044824Z","signature_b64":"K2xoVrkBw5s6+rkLLWUJjtChpANCFfJAzdpA3PnDrNd6ko5mQth7Pe+J1QIR06TpALHhydQUcPuxM6NVi2HuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1d43e27b14956dcc8d2f07b0260b0283694741c3c578aa3252460da23c7c238","last_reissued_at":"2026-05-18T01:30:26.044141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:26.044141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.8279","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MY5X5Clx0Bq/Z7bWvFxMk+8yAdToNruBet5HVqT5j/zaKB++H27yzTaRVppcabu0vOQzoJbXMSAQzTDO2JrFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:34:29.968151Z"},"content_sha256":"834c46fb83a5eb9ce9aa9ac0c5e08a396379016e43bb17f2e8d5f012d3efa12a","schema_version":"1.0","event_id":"sha256:834c46fb83a5eb9ce9aa9ac0c5e08a396379016e43bb17f2e8d5f012d3efa12a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YHKD4J5RJFLNZSGS6B5QEYFQFA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy coherent adjunctions and the formal theory of monads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Dominic Verity, Emily Riehl","submitted_at":"2013-10-30T19:29:24Z","abstract_excerpt":"In this paper, we introduce a cofibrant simplicial category that we call the free homotopy coherent adjunction and characterize its n-arrows using a graphical calculus that we develop here. The hom-spaces are appropriately fibrant, indeed are nerves of categories, which indicates that all of the expected coherence equations in each dimension are present. To justify our terminology, we prove that any adjunction of quasi-categories extends to a homotopy coherent adjunction and furthermore that these extensions are homotopically unique in the sense that the relevant spaces of extensions are contr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8279","kind":"arxiv","version":4},"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":"2026-05-18T01:30:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mnyiiHkXPGs6ZuwB6pQ2KQ1GUgbs9dnOJ2KadMX0B48B0P1eV07NJz6huqaBKZUc0jPX6hkFTNweezfDRmNBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:34:29.968506Z"},"content_sha256":"9f45f3124f61e43a759ee13630c65aa84cacde662cdb1b3ba104143a0d7143f3","schema_version":"1.0","event_id":"sha256:9f45f3124f61e43a759ee13630c65aa84cacde662cdb1b3ba104143a0d7143f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YHKD4J5RJFLNZSGS6B5QEYFQFA/bundle.json","state_url":"https://pith.science/pith/YHKD4J5RJFLNZSGS6B5QEYFQFA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YHKD4J5RJFLNZSGS6B5QEYFQFA/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":"2026-05-31T02:34:29Z","links":{"resolver":"https://pith.science/pith/YHKD4J5RJFLNZSGS6B5QEYFQFA","bundle":"https://pith.science/pith/YHKD4J5RJFLNZSGS6B5QEYFQFA/bundle.json","state":"https://pith.science/pith/YHKD4J5RJFLNZSGS6B5QEYFQFA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YHKD4J5RJFLNZSGS6B5QEYFQFA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YHKD4J5RJFLNZSGS6B5QEYFQFA","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":"e0a41e42d4348e5ac6b6690bd244e30d8c0b0661cd4b5ee692dc63d38fe8670a","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-30T19:29:24Z","title_canon_sha256":"a06a685370739ebd46088a85b87f8b843864bfab20af4295f860deb5c5d525d8"},"schema_version":"1.0","source":{"id":"1310.8279","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8279","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8279v4","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8279","created_at":"2026-05-18T01:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"YHKD4J5RJFLN","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YHKD4J5RJFLNZSGS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YHKD4J5R","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:9f45f3124f61e43a759ee13630c65aa84cacde662cdb1b3ba104143a0d7143f3","target":"graph","created_at":"2026-05-18T01:30:26Z","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"},"paper":{"abstract_excerpt":"In this paper, we introduce a cofibrant simplicial category that we call the free homotopy coherent adjunction and characterize its n-arrows using a graphical calculus that we develop here. The hom-spaces are appropriately fibrant, indeed are nerves of categories, which indicates that all of the expected coherence equations in each dimension are present. To justify our terminology, we prove that any adjunction of quasi-categories extends to a homotopy coherent adjunction and furthermore that these extensions are homotopically unique in the sense that the relevant spaces of extensions are contr","authors_text":"Dominic Verity, Emily Riehl","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-30T19:29:24Z","title":"Homotopy coherent adjunctions and the formal theory of monads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8279","kind":"arxiv","version":4},"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":"sha256:834c46fb83a5eb9ce9aa9ac0c5e08a396379016e43bb17f2e8d5f012d3efa12a","target":"record","created_at":"2026-05-18T01:30:26Z","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":"e0a41e42d4348e5ac6b6690bd244e30d8c0b0661cd4b5ee692dc63d38fe8670a","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-30T19:29:24Z","title_canon_sha256":"a06a685370739ebd46088a85b87f8b843864bfab20af4295f860deb5c5d525d8"},"schema_version":"1.0","source":{"id":"1310.8279","kind":"arxiv","version":4}},"canonical_sha256":"c1d43e27b14956dcc8d2f07b0260b0283694741c3c578aa3252460da23c7c238","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1d43e27b14956dcc8d2f07b0260b0283694741c3c578aa3252460da23c7c238","first_computed_at":"2026-05-18T01:30:26.044141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:26.044141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2xoVrkBw5s6+rkLLWUJjtChpANCFfJAzdpA3PnDrNd6ko5mQth7Pe+J1QIR06TpALHhydQUcPuxM6NVi2HuBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:26.044824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8279","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:834c46fb83a5eb9ce9aa9ac0c5e08a396379016e43bb17f2e8d5f012d3efa12a","sha256:9f45f3124f61e43a759ee13630c65aa84cacde662cdb1b3ba104143a0d7143f3"],"state_sha256":"4c1b6053749f3b9953db972b033f2ca9e65ca26da8fe829df80d20fccb4d4225"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xrhaldwLe+ynBiKI5Njd9Wj7qbmEXppyxXz1KC8myn1Wqf8EwEVkOSsDgYcoRxjRoNPdSUnHx5Gz96+t8jxBAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:34:29.970653Z","bundle_sha256":"d6af6b2bd979594d2becd81b09080467cfc93a9cdc32739cda35dfe3f486455d"}}