{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:6YFX36ZEHECNRRW7EJAS6OTOGL","short_pith_number":"pith:6YFX36ZE","schema_version":"1.0","canonical_sha256":"f60b7dfb243904d8c6df22412f3a6e32f7a1b52d90f0bf55a8da8f286b837262","source":{"kind":"arxiv","id":"alg-geom/9704006","version":2},"attestation_state":"computed","paper":{"title":"A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van Kampen","license":"","headline":"","cross_cats":["math.AG","math.QA","q-alg"],"primary_cat":"alg-geom","authors_text":"Carlos Simpson","submitted_at":"1997-04-10T07:58:36Z","abstract_excerpt":"We define a closed model category containing the $n$-nerves defined by Tamsamani, and admitting internal $Hom$. This allows us to construct the $n+1$-category $nCAT$ by taking the internal $Hom$ for fibrant objects. We prove a generalized Seifert-Van Kampen theorem for Tamsamani's Poincar\\'e $n$-groupoid of a topological space. We give a still-speculative discussion of $n$-stacks, and similarly of comparison with other possible definitions of $n$-category."},"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":"alg-geom/9704006","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-04-10T07:58:36Z","cross_cats_sorted":["math.AG","math.QA","q-alg"],"title_canon_sha256":"9c0fe12b887e37947baa2ae9678793346cf4f6883dc3c1fa03efa7c544aa5995","abstract_canon_sha256":"4d61fae61e43fd67eeb70435f8ba680f1f815ac2e9fefbccec02c782b11c18ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:07:37.055999Z","signature_b64":"f6SSjOkbTl/meCMoNV87FrNuQl2SILMpc2QfYmpanlxmkzV/0r0uQFYuKwPh6Noz6V9p6leKV5CABOhpOu7JBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f60b7dfb243904d8c6df22412f3a6e32f7a1b52d90f0bf55a8da8f286b837262","last_reissued_at":"2026-07-04T15:07:37.055624Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:07:37.055624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A closed model structure for $n$-categories, internal $Hom$, $n$-stacks and generalized Seifert-Van Kampen","license":"","headline":"","cross_cats":["math.AG","math.QA","q-alg"],"primary_cat":"alg-geom","authors_text":"Carlos Simpson","submitted_at":"1997-04-10T07:58:36Z","abstract_excerpt":"We define a closed model category containing the $n$-nerves defined by Tamsamani, and admitting internal $Hom$. This allows us to construct the $n+1$-category $nCAT$ by taking the internal $Hom$ for fibrant objects. We prove a generalized Seifert-Van Kampen theorem for Tamsamani's Poincar\\'e $n$-groupoid of a topological space. We give a still-speculative discussion of $n$-stacks, and similarly of comparison with other possible definitions of $n$-category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9704006","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/alg-geom/9704006/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":"alg-geom/9704006","created_at":"2026-07-04T15:07:37.055689+00:00"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9704006v2","created_at":"2026-07-04T15:07:37.055689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9704006","created_at":"2026-07-04T15:07:37.055689+00:00"},{"alias_kind":"pith_short_12","alias_value":"6YFX36ZEHECN","created_at":"2026-07-04T15:07:37.055689+00:00"},{"alias_kind":"pith_short_16","alias_value":"6YFX36ZEHECNRRW7","created_at":"2026-07-04T15:07:37.055689+00:00"},{"alias_kind":"pith_short_8","alias_value":"6YFX36ZE","created_at":"2026-07-04T15:07:37.055689+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2606.29373","citing_title":"An Oriented Street--Roberts Conjecture","ref_index":64,"is_internal_anchor":true},{"citing_arxiv_id":"2603.09903","citing_title":"Homotopy Posets, Postnikov Towers, and Hypercompletions of $\\infty$-Categories","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL","json":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL.json","graph_json":"https://pith.science/api/pith-number/6YFX36ZEHECNRRW7EJAS6OTOGL/graph.json","events_json":"https://pith.science/api/pith-number/6YFX36ZEHECNRRW7EJAS6OTOGL/events.json","paper":"https://pith.science/paper/6YFX36ZE"},"agent_actions":{"view_html":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL","download_json":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL.json","view_paper":"https://pith.science/paper/6YFX36ZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=alg-geom/9704006&json=true","fetch_graph":"https://pith.science/api/pith-number/6YFX36ZEHECNRRW7EJAS6OTOGL/graph.json","fetch_events":"https://pith.science/api/pith-number/6YFX36ZEHECNRRW7EJAS6OTOGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL/action/storage_attestation","attest_author":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL/action/author_attestation","sign_citation":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL/action/citation_signature","submit_replication":"https://pith.science/pith/6YFX36ZEHECNRRW7EJAS6OTOGL/action/replication_record"}},"created_at":"2026-07-04T15:07:37.055689+00:00","updated_at":"2026-07-04T15:07:37.055689+00:00"}