{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:76KV4DU3WTWJXTST2MDUBXE4RK","short_pith_number":"pith:76KV4DU3","schema_version":"1.0","canonical_sha256":"ff955e0e9bb4ec9bce53d30740dc9c8a85a4910741d188e9c57a3a75ff3b2643","source":{"kind":"arxiv","id":"1204.5101","version":3},"attestation_state":"computed","paper":{"title":"Segal-type algebraic models of n-types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"David Blanc, Simona Paoli","submitted_at":"2012-04-23T16:38:25Z","abstract_excerpt":"For each n\\geq 1 we introduce two new Segal-type models of n-types of topological spaces: weakly globular n-fold groupoids, and a lax version of these. We show that any n-type can be represented up to homotopy by such models via an explicit algebraic fundamental n-fold groupoid functor. We compare these models to Tamsamani's weak n-groupoids, and extract from them a model for (k-1)connected n-types"},"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":"1204.5101","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-23T16:38:25Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"e2062d2973034da686d65e453904cf7e2caf363ea5e7f4ef42552327610c5670","abstract_canon_sha256":"ef40e0a5509c6e60710ca17caa4f4de3689ec896ad5b0a073c6d8a50c722bfed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:38.612901Z","signature_b64":"12V3QgNPcHVEXJqeR19RbPjWNwZvr58fNyCW3BY7gusQ5iEUAu746+55EpGt9Rmc/SW8DeArM6oyJxA9ZiHQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff955e0e9bb4ec9bce53d30740dc9c8a85a4910741d188e9c57a3a75ff3b2643","last_reissued_at":"2026-05-18T02:03:38.612361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:38.612361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Segal-type algebraic models of n-types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"David Blanc, Simona Paoli","submitted_at":"2012-04-23T16:38:25Z","abstract_excerpt":"For each n\\geq 1 we introduce two new Segal-type models of n-types of topological spaces: weakly globular n-fold groupoids, and a lax version of these. We show that any n-type can be represented up to homotopy by such models via an explicit algebraic fundamental n-fold groupoid functor. We compare these models to Tamsamani's weak n-groupoids, and extract from them a model for (k-1)connected n-types"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5101","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1204.5101","created_at":"2026-05-18T02:03:38.612456+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.5101v3","created_at":"2026-05-18T02:03:38.612456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5101","created_at":"2026-05-18T02:03:38.612456+00:00"},{"alias_kind":"pith_short_12","alias_value":"76KV4DU3WTWJ","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"76KV4DU3WTWJXTST","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"76KV4DU3","created_at":"2026-05-18T12:26:56.085431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK","json":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK.json","graph_json":"https://pith.science/api/pith-number/76KV4DU3WTWJXTST2MDUBXE4RK/graph.json","events_json":"https://pith.science/api/pith-number/76KV4DU3WTWJXTST2MDUBXE4RK/events.json","paper":"https://pith.science/paper/76KV4DU3"},"agent_actions":{"view_html":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK","download_json":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK.json","view_paper":"https://pith.science/paper/76KV4DU3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.5101&json=true","fetch_graph":"https://pith.science/api/pith-number/76KV4DU3WTWJXTST2MDUBXE4RK/graph.json","fetch_events":"https://pith.science/api/pith-number/76KV4DU3WTWJXTST2MDUBXE4RK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK/action/storage_attestation","attest_author":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK/action/author_attestation","sign_citation":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK/action/citation_signature","submit_replication":"https://pith.science/pith/76KV4DU3WTWJXTST2MDUBXE4RK/action/replication_record"}},"created_at":"2026-05-18T02:03:38.612456+00:00","updated_at":"2026-05-18T02:03:38.612456+00:00"}