{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:KLMORIXNPB2OHWYAXK4LNCNYW4","short_pith_number":"pith:KLMORIXN","schema_version":"1.0","canonical_sha256":"52d8e8a2ed7874e3db00bab8b689b8b7150c1beb4845260b11a514fe2a29f912","source":{"kind":"arxiv","id":"2509.10288","version":1},"attestation_state":"computed","paper":{"title":"Derived mapping spaces of $\\infty$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Chris Kapulkin, Daniel Carranza, Kensuke Arakawa","submitted_at":"2025-09-12T14:28:07Z","abstract_excerpt":"We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for $\\infty$-categories, and allows us to provide a unified framework for analyzing mapping spaces in localizations of ($\\infty$-)categories. As an application, we give a sufficient condition for when a cubical or simplicial category is the localization of its underlying category at homotopy equivalences."},"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":"2509.10288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-09-12T14:28:07Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"c3d0197706314938f1a0ba43fb7683663f9ace763b9b3c9b589d65ab74dc163e","abstract_canon_sha256":"d3e723923113ada425132b2188c5ad11789dc77a458e6c94375ec072fcfec4d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:11:06.543973Z","signature_b64":"kleNjEill5QJIJ6N3tWN/uwmFWq9VrfYcz2wdPyWq0lpV6EnC9Jm9ZGhfrELnaHv+HyHgIK4V6cGx15TYfXBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52d8e8a2ed7874e3db00bab8b689b8b7150c1beb4845260b11a514fe2a29f912","last_reissued_at":"2026-07-05T12:11:06.543444Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:11:06.543444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derived mapping spaces of $\\infty$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Chris Kapulkin, Daniel Carranza, Kensuke Arakawa","submitted_at":"2025-09-12T14:28:07Z","abstract_excerpt":"We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for $\\infty$-categories, and allows us to provide a unified framework for analyzing mapping spaces in localizations of ($\\infty$-)categories. As an application, we give a sufficient condition for when a cubical or simplicial category is the localization of its underlying category at homotopy equivalences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.10288","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.10288/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":"2509.10288","created_at":"2026-07-05T12:11:06.543513+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.10288v1","created_at":"2026-07-05T12:11:06.543513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.10288","created_at":"2026-07-05T12:11:06.543513+00:00"},{"alias_kind":"pith_short_12","alias_value":"KLMORIXNPB2O","created_at":"2026-07-05T12:11:06.543513+00:00"},{"alias_kind":"pith_short_16","alias_value":"KLMORIXNPB2OHWYA","created_at":"2026-07-05T12:11:06.543513+00:00"},{"alias_kind":"pith_short_8","alias_value":"KLMORIXN","created_at":"2026-07-05T12:11:06.543513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.11895","citing_title":"Relative dendroidal Rezk nerve and applications","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04959","citing_title":"The discrete homotopy hypothesis for directed graphs","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4","json":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4.json","graph_json":"https://pith.science/api/pith-number/KLMORIXNPB2OHWYAXK4LNCNYW4/graph.json","events_json":"https://pith.science/api/pith-number/KLMORIXNPB2OHWYAXK4LNCNYW4/events.json","paper":"https://pith.science/paper/KLMORIXN"},"agent_actions":{"view_html":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4","download_json":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4.json","view_paper":"https://pith.science/paper/KLMORIXN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.10288&json=true","fetch_graph":"https://pith.science/api/pith-number/KLMORIXNPB2OHWYAXK4LNCNYW4/graph.json","fetch_events":"https://pith.science/api/pith-number/KLMORIXNPB2OHWYAXK4LNCNYW4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4/action/storage_attestation","attest_author":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4/action/author_attestation","sign_citation":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4/action/citation_signature","submit_replication":"https://pith.science/pith/KLMORIXNPB2OHWYAXK4LNCNYW4/action/replication_record"}},"created_at":"2026-07-05T12:11:06.543513+00:00","updated_at":"2026-07-05T12:11:06.543513+00:00"}