{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:6RW3ZVPLGYCTYMA6Q5LLXQBDTY","short_pith_number":"pith:6RW3ZVPL","schema_version":"1.0","canonical_sha256":"f46dbcd5eb36053c301e8756bbc0239e24bc5bf08835253f04caca99ee67e595","source":{"kind":"arxiv","id":"2408.14335","version":2},"attestation_state":"computed","paper":{"title":"Homotopy coherent companionships and conjunctions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Jaco Ruit","submitted_at":"2024-08-26T15:03:22Z","abstract_excerpt":"We demonstrate that companionships and conjunctions in double $\\infty$-categories -- and more generally, in double Segal spaces -- extend to functors out of the free-living companionship and conjunction respectively. Specifically, we prove that these extensions are (homotopically) unique: the corresponding spaces of extensions are contractible under suitable completeness assumptions. The developed theory is then put to use to give a characterization of companions and conjoints in functor double Segal spaces in terms of so-called companionable and conjointable 2-cells. We end with an applicatio"},"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":"2408.14335","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2024-08-26T15:03:22Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"1a52a80e1c69741033b4ca5a69350691748dbd8101cd5aca704113c738877874","abstract_canon_sha256":"5ba0ea38c80778a8038960cf5fbc8367df11fd7383c61ea8973bbbbd55e19c93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:45:54.648682Z","signature_b64":"1f54B7EVCJ/De5bOT5gJEfxzpXiOuhiyvESueKeNfxUq6Pjnn7MT4HXXIJ81GH9BqTcqilD1XbcQs40ZnY7HCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f46dbcd5eb36053c301e8756bbc0239e24bc5bf08835253f04caca99ee67e595","last_reissued_at":"2026-07-05T10:45:54.648257Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:45:54.648257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homotopy coherent companionships and conjunctions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Jaco Ruit","submitted_at":"2024-08-26T15:03:22Z","abstract_excerpt":"We demonstrate that companionships and conjunctions in double $\\infty$-categories -- and more generally, in double Segal spaces -- extend to functors out of the free-living companionship and conjunction respectively. Specifically, we prove that these extensions are (homotopically) unique: the corresponding spaces of extensions are contractible under suitable completeness assumptions. The developed theory is then put to use to give a characterization of companions and conjoints in functor double Segal spaces in terms of so-called companionable and conjointable 2-cells. We end with an applicatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.14335","kind":"arxiv","version":2},"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/2408.14335/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":"2408.14335","created_at":"2026-07-05T10:45:54.648318+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.14335v2","created_at":"2026-07-05T10:45:54.648318+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.14335","created_at":"2026-07-05T10:45:54.648318+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RW3ZVPLGYCT","created_at":"2026-07-05T10:45:54.648318+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RW3ZVPLGYCTYMA6","created_at":"2026-07-05T10:45:54.648318+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RW3ZVPL","created_at":"2026-07-05T10:45:54.648318+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.07807","citing_title":"On the squares functor and the Gaitsgory-Rozenblyum conjectures","ref_index":21,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY","json":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY.json","graph_json":"https://pith.science/api/pith-number/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/graph.json","events_json":"https://pith.science/api/pith-number/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/events.json","paper":"https://pith.science/paper/6RW3ZVPL"},"agent_actions":{"view_html":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY","download_json":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY.json","view_paper":"https://pith.science/paper/6RW3ZVPL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.14335&json=true","fetch_graph":"https://pith.science/api/pith-number/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/graph.json","fetch_events":"https://pith.science/api/pith-number/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/action/storage_attestation","attest_author":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/action/author_attestation","sign_citation":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/action/citation_signature","submit_replication":"https://pith.science/pith/6RW3ZVPLGYCTYMA6Q5LLXQBDTY/action/replication_record"}},"created_at":"2026-07-05T10:45:54.648318+00:00","updated_at":"2026-07-05T10:45:54.648318+00:00"}