{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:76KV4DU3WTWJXTST2MDUBXE4RK","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":"ef40e0a5509c6e60710ca17caa4f4de3689ec896ad5b0a073c6d8a50c722bfed","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-23T16:38:25Z","title_canon_sha256":"e2062d2973034da686d65e453904cf7e2caf363ea5e7f4ef42552327610c5670"},"schema_version":"1.0","source":{"id":"1204.5101","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5101","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5101v3","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5101","created_at":"2026-05-18T02:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"76KV4DU3WTWJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"76KV4DU3WTWJXTST","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"76KV4DU3","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:32eae38ed796e7ce0f4f4b91119976a65e5cf7a9f7375fa832f8424409f629cc","target":"graph","created_at":"2026-05-18T02:03:38Z","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":"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","authors_text":"David Blanc, Simona Paoli","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-23T16:38:25Z","title":"Segal-type algebraic models of n-types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5101","kind":"arxiv","version":3},"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":"sha256:662a0c495dddfa98ef9fd7642d6c4812bb1392eecd37bc62d6c0a7b9d99e3065","target":"record","created_at":"2026-05-18T02:03:38Z","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":"ef40e0a5509c6e60710ca17caa4f4de3689ec896ad5b0a073c6d8a50c722bfed","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-23T16:38:25Z","title_canon_sha256":"e2062d2973034da686d65e453904cf7e2caf363ea5e7f4ef42552327610c5670"},"schema_version":"1.0","source":{"id":"1204.5101","kind":"arxiv","version":3}},"canonical_sha256":"ff955e0e9bb4ec9bce53d30740dc9c8a85a4910741d188e9c57a3a75ff3b2643","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff955e0e9bb4ec9bce53d30740dc9c8a85a4910741d188e9c57a3a75ff3b2643","first_computed_at":"2026-05-18T02:03:38.612361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:38.612361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"12V3QgNPcHVEXJqeR19RbPjWNwZvr58fNyCW3BY7gusQ5iEUAu746+55EpGt9Rmc/SW8DeArM6oyJxA9ZiHQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:38.612901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5101","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:662a0c495dddfa98ef9fd7642d6c4812bb1392eecd37bc62d6c0a7b9d99e3065","sha256:32eae38ed796e7ce0f4f4b91119976a65e5cf7a9f7375fa832f8424409f629cc"],"state_sha256":"b79b9ee418d84706097dd967497700063894c397b3c214af03763749a1fbdca3"}