{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TCI4ILLF4T3C3GLYYPOV2JB3LZ","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":"08d486a2c0843a665f469ab878f9d6cefb18ecce8b85b6bd3f417b3a87898efc","cross_cats_sorted":["math.CO","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-06-19T19:08:45Z","title_canon_sha256":"3466a5c5709fb3b55d25edd0019fbe660b369eb29be09aca92a42b214e38e54e"},"schema_version":"1.0","source":{"id":"1106.3772","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3772","created_at":"2026-05-18T01:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3772v4","created_at":"2026-05-18T01:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3772","created_at":"2026-05-18T01:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"TCI4ILLF4T3C","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TCI4ILLF4T3C3GLY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TCI4ILLF","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:7e9feef3c7664d05956d79d49108fc9921325569093ecb341dee8304116fd3c7","target":"graph","created_at":"2026-05-18T01:04:35Z","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":"The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonz\\'alez, and Rudyak [1009.1851] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it was shown that the classifying space (order complex) of the face poset of a totally normal regular cellular stratified space $X$ can be embedded in $X$ as a strong deformation retract.\n  Here we elaborate on this idea and develop the theory of cellular stratified spaces. We introduce the notion of cylindrically normal cellular stratified spaces and associate a","authors_text":"Dai Tamaki","cross_cats":["math.CO","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-06-19T19:08:45Z","title":"Cellular Stratified Spaces I: Face Categories and Classifying Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3772","kind":"arxiv","version":4},"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":"sha256:91de7e24a45ff2da7884e4a86ff4a77c57700fe4027431ed94be9dd8be1dada0","target":"record","created_at":"2026-05-18T01:04:35Z","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":"08d486a2c0843a665f469ab878f9d6cefb18ecce8b85b6bd3f417b3a87898efc","cross_cats_sorted":["math.CO","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-06-19T19:08:45Z","title_canon_sha256":"3466a5c5709fb3b55d25edd0019fbe660b369eb29be09aca92a42b214e38e54e"},"schema_version":"1.0","source":{"id":"1106.3772","kind":"arxiv","version":4}},"canonical_sha256":"9891c42d65e4f62d9978c3dd5d243b5e6973edfed0e7efe911467a25f10bcf98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9891c42d65e4f62d9978c3dd5d243b5e6973edfed0e7efe911467a25f10bcf98","first_computed_at":"2026-05-18T01:04:35.501677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:35.501677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nqAkOFHVrQY/tbJPdDboSE+X7IYem+6Q+0Q9vNZtZbo33M+7DAe7dkEc+HEWeT/ee9rNVHadz9Rsre1VHKEFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:35.502395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3772","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91de7e24a45ff2da7884e4a86ff4a77c57700fe4027431ed94be9dd8be1dada0","sha256:7e9feef3c7664d05956d79d49108fc9921325569093ecb341dee8304116fd3c7"],"state_sha256":"5c279bd544163ef34c888d309aa75d6c74c477d29915d947423514e1a75ebef2"}