{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:WHAFZAMXT5BWAQMAAZ6M5G6RE3","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":"0cfb28c9eef603880b2cf62d42b215d646cb4029a1da5bf11630208dfdc6216e","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-29T15:09:18Z","title_canon_sha256":"e09b870ea97abb132a0cc647c474ce62008a07ff1dadd4366b1bef799ba5cdb6"},"schema_version":"1.0","source":{"id":"0808.4108","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.4108","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0808.4108v2","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.4108","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"WHAFZAMXT5BW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"WHAFZAMXT5BWAQMA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"WHAFZAMX","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f044e53b48e5e5d9bccfd08fb0a5153ee1163a1f1c2b97677b5cb4e32de5fbb2","target":"graph","created_at":"2026-05-18T02:41:51Z","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":"We construct a cofibrantly generated Quillen model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. This is an n-fold analogue to Thomason's Quillen model structure on Cat. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, we completely prove that the un","authors_text":"Simona Paoli, Thomas M. Fiore","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-29T15:09:18Z","title":"A Thomason Model Structure on the Category of Small n-fold Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.4108","kind":"arxiv","version":2},"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:db69198ff12c9fa939c9bda043c3a5304ce14e0fa9e74d36e0239b42ed60df51","target":"record","created_at":"2026-05-18T02:41:51Z","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":"0cfb28c9eef603880b2cf62d42b215d646cb4029a1da5bf11630208dfdc6216e","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-29T15:09:18Z","title_canon_sha256":"e09b870ea97abb132a0cc647c474ce62008a07ff1dadd4366b1bef799ba5cdb6"},"schema_version":"1.0","source":{"id":"0808.4108","kind":"arxiv","version":2}},"canonical_sha256":"b1c05c81979f43604180067cce9bd126ff81e1e3ba684800c7004997d755e96e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1c05c81979f43604180067cce9bd126ff81e1e3ba684800c7004997d755e96e","first_computed_at":"2026-05-18T02:41:51.541908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.541908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n6TlEml4xPF+t4C8xIuhh9DINJljGyFEwrR++xkUMZMN9q9KrrQojP3DcLPqIFczg6bFWj3DxJy90JnsAoroCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.542385Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.4108","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db69198ff12c9fa939c9bda043c3a5304ce14e0fa9e74d36e0239b42ed60df51","sha256:f044e53b48e5e5d9bccfd08fb0a5153ee1163a1f1c2b97677b5cb4e32de5fbb2"],"state_sha256":"8134b70037ea355d2ff770683583419d6109ccbf1d56d33461e66b8f3cd86e74"}