{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:IHJA6G2PLNYRL2JVUQSJRXAHBX","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":"13b6e3a234b63e29b50ae99bfab29101cd86c4491671d2a07d534af78a7fd2df","cross_cats_sorted":["cs.FL","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2023-12-29T12:09:35Z","title_canon_sha256":"39b8e1e893f1ea9ff51712309df01c4a55d83c9126efacb5e971cce02aa6a2e9"},"schema_version":"1.0","source":{"id":"2405.14703","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.14703","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"2405.14703v4","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14703","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"IHJA6G2PLNYR","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_16","alias_value":"IHJA6G2PLNYRL2JV","created_at":"2026-07-05T11:06:08Z"},{"alias_kind":"pith_short_8","alias_value":"IHJA6G2P","created_at":"2026-07-05T11:06:08Z"}],"graph_snapshots":[{"event_id":"sha256:381775f78f3c82508320c283ae914195c411393f11c90cb077dc512471b21c84","target":"graph","created_at":"2026-07-05T11:06:08Z","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/2405.14703/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop fibrational perspectives on context-free grammars and on nondeterministic finite-state automata over categories and operads. A generalized CFG is a functor from a free colored operad (aka multicategory) generated by a pointed finite species into an arbitrary base operad: this encompasses classical CFGs by taking the base to be a certain operad constructed from a free monoid, as an instance of a more general construction of an \\emph{operad of spliced arrows} $\\mathcal{W}\\,\\mathcal{C}$ for any category $\\mathcal{C}$. A generalized NFA is a functor from an arbitrary bipointed category ","authors_text":"Noam Zeilberger, Paul-Andr\\'e Melli\\`es","cross_cats":["cs.FL","cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2023-12-29T12:09:35Z","title":"The categorical contours of the Chomsky-Sch\\\"utzenberger representation theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14703","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":"sha256:9e5602f84876c65ab6c4bd65537e0f2896f7340b9e25f426d256ebc8053d0a4e","target":"record","created_at":"2026-07-05T11:06:08Z","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":"13b6e3a234b63e29b50ae99bfab29101cd86c4491671d2a07d534af78a7fd2df","cross_cats_sorted":["cs.FL","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2023-12-29T12:09:35Z","title_canon_sha256":"39b8e1e893f1ea9ff51712309df01c4a55d83c9126efacb5e971cce02aa6a2e9"},"schema_version":"1.0","source":{"id":"2405.14703","kind":"arxiv","version":4}},"canonical_sha256":"41d20f1b4f5b7115e935a42498dc070dc492ab0fe2b12810838924507c19b8ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41d20f1b4f5b7115e935a42498dc070dc492ab0fe2b12810838924507c19b8ef","first_computed_at":"2026-07-05T11:06:08.051169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:08.051169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5OYHFEeaYhwzDdJlLqy2vVA4EMsQtlEP+E580HQ8cLE4/VPUFxGuADvJsanRHn3KsAObgU8ebDCW59lZey7aAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:08.051680Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.14703","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e5602f84876c65ab6c4bd65537e0f2896f7340b9e25f426d256ebc8053d0a4e","sha256:381775f78f3c82508320c283ae914195c411393f11c90cb077dc512471b21c84"],"state_sha256":"7d50699cc7a3bf734551244da14438273ff6c98abce024b6d2840c6cdc563cc9"}