{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TV5F2W7R5ZVS3YCY7VILSV7SHT","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":"4f73315506d7567e592ae09d286d8656cdb27727f6a8056de08da52ad0d1faa3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-05-20T02:49:27Z","title_canon_sha256":"dbd30b1d33389544d9418685dc8bc98334dfc2444bf10982548006e6a461d2d9"},"schema_version":"1.0","source":{"id":"2505.13850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13850","created_at":"2026-07-05T12:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13850v1","created_at":"2026-07-05T12:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13850","created_at":"2026-07-05T12:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"TV5F2W7R5ZVS","created_at":"2026-07-05T12:00:01Z"},{"alias_kind":"pith_short_16","alias_value":"TV5F2W7R5ZVS3YCY","created_at":"2026-07-05T12:00:01Z"},{"alias_kind":"pith_short_8","alias_value":"TV5F2W7R","created_at":"2026-07-05T12:00:01Z"}],"graph_snapshots":[{"event_id":"sha256:46c635a460299418fcb75a5160cdbd901f218c4c466b5908f162f85bc8207534","target":"graph","created_at":"2026-07-05T12:00:01Z","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/2505.13850/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the notion of involutive weak cubical $\\omega$-categories via Penon's approach: as algebras for the monad induced by the free involutive strict $\\omega$-category functor on cubical $\\omega$-sets. A few examples of involutive weak cubical $\\omega$-categories are provided.","authors_text":"Paolo Bertozzini, Paratat Bejrakarbum, Supaporn Theesoongnern","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-05-20T02:49:27Z","title":"Involutive Weak Cubical $\\omega$-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13850","kind":"arxiv","version":1},"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:e76c452a195b93a4869c9cf0f96a3628a456e1dda2d3e930a7b8cfc3db7a0187","target":"record","created_at":"2026-07-05T12:00:01Z","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":"4f73315506d7567e592ae09d286d8656cdb27727f6a8056de08da52ad0d1faa3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-05-20T02:49:27Z","title_canon_sha256":"dbd30b1d33389544d9418685dc8bc98334dfc2444bf10982548006e6a461d2d9"},"schema_version":"1.0","source":{"id":"2505.13850","kind":"arxiv","version":1}},"canonical_sha256":"9d7a5d5bf1ee6b2de058fd50b957f23cdc67c9429fa722a61f3337f4648a1ad3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d7a5d5bf1ee6b2de058fd50b957f23cdc67c9429fa722a61f3337f4648a1ad3","first_computed_at":"2026-07-05T12:00:01.267655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:00:01.267655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FWzp6n/BtINZbhqYbcb0c7nUlPxXwSmuApoLQaee9eHW/DRckJ9xPkXrxhIbEpGJDnR1UseHAp9aH/TDdF/lBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:00:01.267999Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e76c452a195b93a4869c9cf0f96a3628a456e1dda2d3e930a7b8cfc3db7a0187","sha256:46c635a460299418fcb75a5160cdbd901f218c4c466b5908f162f85bc8207534"],"state_sha256":"de21395a551ded9dbf7ea2c83c081497cbdad8c80ec9228a5b248095f4e0afed"}