{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VR4X6MQWMQZCCA4AELQSCKYAJ4","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":"9def6b84756655d120b8fcf1bf07a0ca94b06f9504e7aad56676e24bd3da0969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-06-08T10:09:37Z","title_canon_sha256":"d9186c91e1275230cbf4814f040109ea73bbcaab4c49052e5c713b6b75496ba8"},"schema_version":"1.0","source":{"id":"2406.05425","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.05425","created_at":"2026-07-05T09:39:23Z"},{"alias_kind":"arxiv_version","alias_value":"2406.05425v2","created_at":"2026-07-05T09:39:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.05425","created_at":"2026-07-05T09:39:23Z"},{"alias_kind":"pith_short_12","alias_value":"VR4X6MQWMQZC","created_at":"2026-07-05T09:39:23Z"},{"alias_kind":"pith_short_16","alias_value":"VR4X6MQWMQZCCA4A","created_at":"2026-07-05T09:39:23Z"},{"alias_kind":"pith_short_8","alias_value":"VR4X6MQW","created_at":"2026-07-05T09:39:23Z"}],"graph_snapshots":[{"event_id":"sha256:a5e95a552518910f76955274b4d51ae8944cdfb52aa664143a3ea0ca57c2cff9","target":"graph","created_at":"2026-07-05T09:39:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.05425/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This text is dedicated to the development of the theory of $(\\infty,\\omega)$-categories. We present generalizations of standard results from category theory, such as the lax Grothendieck construction, the Yoneda lemma, lax (co)limits and lax Kan extensions, among others.","authors_text":"F\\'elix Loubaton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-06-08T10:09:37Z","title":"Categorical Theory of $(\\infty,\\omega)$-Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.05425","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:a6b67d42b0ed90eb8a18293bee71ad0d025d60cfb6314cbb8e2a0a61fad65a92","target":"record","created_at":"2026-07-05T09:39:23Z","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":"9def6b84756655d120b8fcf1bf07a0ca94b06f9504e7aad56676e24bd3da0969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-06-08T10:09:37Z","title_canon_sha256":"d9186c91e1275230cbf4814f040109ea73bbcaab4c49052e5c713b6b75496ba8"},"schema_version":"1.0","source":{"id":"2406.05425","kind":"arxiv","version":2}},"canonical_sha256":"ac797f3216643221038022e1212b004f10e200fae0e5ad8b0a6a2e5d439a4ed5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac797f3216643221038022e1212b004f10e200fae0e5ad8b0a6a2e5d439a4ed5","first_computed_at":"2026-07-05T09:39:23.981760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:23.981760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b6nnfJPaCwINASKjnV2XmhVHuI9H+WA4nvmeyjC/+Adh0l3QSh5REPyQk2LhjnZmHMvgRin/L/u1qj6almPYDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:23.982195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.05425","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6b67d42b0ed90eb8a18293bee71ad0d025d60cfb6314cbb8e2a0a61fad65a92","sha256:a5e95a552518910f76955274b4d51ae8944cdfb52aa664143a3ea0ca57c2cff9"],"state_sha256":"bca8cb98580f3e81673a985ac45c6ea9178bb77766e46c4469c286172c3e9822"}