{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:L463WW4T3223P7NZTTK6VAAUGV","short_pith_number":"pith:L463WW4T","schema_version":"1.0","canonical_sha256":"5f3dbb5b93deb5b7fdb99cd5ea80143556b7d4eef6a62214807db397cd4706b9","source":{"kind":"arxiv","id":"2011.12723","version":1},"attestation_state":"computed","paper":{"title":"On k-invariants for $(\\infty, n)$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Joost Nuiten, Matan Prasma, Yonatan Harpaz","submitted_at":"2020-11-25T13:34:38Z","abstract_excerpt":"Every $(\\infty, n)$-category can be approximated by its tower of homotopy $(m, n)$-categories. In this paper, we prove that the successive stages of this tower are classified by k-invariants, analogously to the classical Postnikov tower for spaces. Our proof relies on an abstract analysis of Postnikov-type towers equipped with k-invariants, and also yields a construction of k-invariants for algebras over $\\infty$-operads and enriched $\\infty$-categories."},"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":"2011.12723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-11-25T13:34:38Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"5f13845c1bce1ec1f99617f25198f0141e75323f57c30f40e38766c2522277e0","abstract_canon_sha256":"fb75ce150da1bf86bfe2b9077945cbe5f13476bb0308d0f75219e31f4b23d5e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:06.107844Z","signature_b64":"npHbHfJXe5Dw9s6fUIvleRa649YdDoJoC2LKMb9ujoGqC3ZWYACg8+k5hQIZ5s4SK6YHn89Ibj72VU4ID+BlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f3dbb5b93deb5b7fdb99cd5ea80143556b7d4eef6a62214807db397cd4706b9","last_reissued_at":"2026-07-05T11:06:06.107355Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:06.107355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On k-invariants for $(\\infty, n)$-categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Joost Nuiten, Matan Prasma, Yonatan Harpaz","submitted_at":"2020-11-25T13:34:38Z","abstract_excerpt":"Every $(\\infty, n)$-category can be approximated by its tower of homotopy $(m, n)$-categories. In this paper, we prove that the successive stages of this tower are classified by k-invariants, analogously to the classical Postnikov tower for spaces. Our proof relies on an abstract analysis of Postnikov-type towers equipped with k-invariants, and also yields a construction of k-invariants for algebras over $\\infty$-operads and enriched $\\infty$-categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.12723","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/2011.12723/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":"2011.12723","created_at":"2026-07-05T11:06:06.107408+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.12723v1","created_at":"2026-07-05T11:06:06.107408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.12723","created_at":"2026-07-05T11:06:06.107408+00:00"},{"alias_kind":"pith_short_12","alias_value":"L463WW4T3223","created_at":"2026-07-05T11:06:06.107408+00:00"},{"alias_kind":"pith_short_16","alias_value":"L463WW4T3223P7NZ","created_at":"2026-07-05T11:06:06.107408+00:00"},{"alias_kind":"pith_short_8","alias_value":"L463WW4T","created_at":"2026-07-05T11:06:06.107408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.16326","citing_title":"Deformation Theory for $(\\infty,n)$-categories","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV","json":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV.json","graph_json":"https://pith.science/api/pith-number/L463WW4T3223P7NZTTK6VAAUGV/graph.json","events_json":"https://pith.science/api/pith-number/L463WW4T3223P7NZTTK6VAAUGV/events.json","paper":"https://pith.science/paper/L463WW4T"},"agent_actions":{"view_html":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV","download_json":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV.json","view_paper":"https://pith.science/paper/L463WW4T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.12723&json=true","fetch_graph":"https://pith.science/api/pith-number/L463WW4T3223P7NZTTK6VAAUGV/graph.json","fetch_events":"https://pith.science/api/pith-number/L463WW4T3223P7NZTTK6VAAUGV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV/action/storage_attestation","attest_author":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV/action/author_attestation","sign_citation":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV/action/citation_signature","submit_replication":"https://pith.science/pith/L463WW4T3223P7NZTTK6VAAUGV/action/replication_record"}},"created_at":"2026-07-05T11:06:06.107408+00:00","updated_at":"2026-07-05T11:06:06.107408+00:00"}