{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OYB2ZZC5BEU4SRB3SOP5TRX7Z2","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":"f5440d19005ed75a970bf431accbc03c3b3c3540eff21ca5342b00957ee3ee5b","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-03-25T09:38:10Z","title_canon_sha256":"e5d5f1b8551d3cf7234c85cd2a97267112e7afa99114bde0ab6de9a830c10a65"},"schema_version":"1.0","source":{"id":"0903.4276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4276","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4276v2","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4276","created_at":"2026-05-18T04:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"OYB2ZZC5BEU4","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OYB2ZZC5BEU4SRB3","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OYB2ZZC5","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:79340491ea4b9d5c7555305aa2b85f47cd2cbb775716d8e8fa37ee96d0a760b1","target":"graph","created_at":"2026-05-18T04:35:55Z","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":"Cattani-Sassone's notion of higher dimensional transition system is interpreted as a small-orthogonality class of a locally finitely presentable topological category of weak higher dimensional transition systems. In particular, the higher dimensional transition system associated with the labelled n-cube turns out to be the free higher dimensional transition system generated by one n-dimensional transition. As a first application of this construction, it is proved that a localization of the category of higher dimensional transition systems is equivalent to a locally finitely presentable reflect","authors_text":"Philippe Gaucher","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-03-25T09:38:10Z","title":"Directed algebraic topology and higher dimensional transition system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4276","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":"sha256:6ce26ce8a0cc9cd586522b1432661126ac092d339df46b9139d718dd1de5e87c","target":"record","created_at":"2026-05-18T04:35:55Z","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":"f5440d19005ed75a970bf431accbc03c3b3c3540eff21ca5342b00957ee3ee5b","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2009-03-25T09:38:10Z","title_canon_sha256":"e5d5f1b8551d3cf7234c85cd2a97267112e7afa99114bde0ab6de9a830c10a65"},"schema_version":"1.0","source":{"id":"0903.4276","kind":"arxiv","version":2}},"canonical_sha256":"7603ace45d0929c9443b939fd9c6ffce95bc4d6545b623b428377339adba4cb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7603ace45d0929c9443b939fd9c6ffce95bc4d6545b623b428377339adba4cb9","first_computed_at":"2026-05-18T04:35:55.294634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:55.294634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gGiA2785uDNYaoaMglrDzOW9VnPXAZ49DX5nX+tKkLgYKCEoXhWi5Bj8MO3rSnBhVm+jU6Bi3E4kC2p8kSgqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:55.295386Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.4276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ce26ce8a0cc9cd586522b1432661126ac092d339df46b9139d718dd1de5e87c","sha256:79340491ea4b9d5c7555305aa2b85f47cd2cbb775716d8e8fa37ee96d0a760b1"],"state_sha256":"536bd93dcafa28f37312a7b1c30bebb516827b1e8386e4b5a62b8d456675b838"}