{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YXTIIFS2ZJ3JQS474ZTN6ELTXD","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":"e1c58c021e4fa234cf7349711ceac1993d8bba155bc57ba50e910ac55e12bda2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2010-06-19T00:22:14Z","title_canon_sha256":"a98403c82fe0377793854bdfa755754b39c4a81eab17bc6ee3a7df8aa5611536"},"schema_version":"1.0","source":{"id":"1006.3825","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3825","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3825v3","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3825","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"YXTIIFS2ZJ3J","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YXTIIFS2ZJ3JQS47","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YXTIIFS2","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:b84c4372c0affa88f8ecb978bb83748163eb70748686d65e5aaa933d6d4594d7","target":"graph","created_at":"2026-05-18T03:52:12Z","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":"Parikh's theorem states that the Parikh image of a context-free language is semilinear or, equivalently, that every context-free language has the same Parikh image as some regular language. We present a very simple construction that, given a context-free grammar, produces a finite automaton recognizing such a regular language.","authors_text":"Javier Esparza, Michael Luttenberger, Pierre Ganty, Stefan Kiefer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2010-06-19T00:22:14Z","title":"Parikh's Theorem: A simple and direct automaton construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3825","kind":"arxiv","version":3},"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:eb9168b81c4c1bcf9ddccc107816729d4fad241d5eec61cb60cac2faeccd910f","target":"record","created_at":"2026-05-18T03:52:12Z","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":"e1c58c021e4fa234cf7349711ceac1993d8bba155bc57ba50e910ac55e12bda2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2010-06-19T00:22:14Z","title_canon_sha256":"a98403c82fe0377793854bdfa755754b39c4a81eab17bc6ee3a7df8aa5611536"},"schema_version":"1.0","source":{"id":"1006.3825","kind":"arxiv","version":3}},"canonical_sha256":"c5e684165aca76984b9fe666df1173b8debc5eb1a16a476fb39d238fa5703b8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5e684165aca76984b9fe666df1173b8debc5eb1a16a476fb39d238fa5703b8d","first_computed_at":"2026-05-18T03:52:12.611356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:12.611356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vBkbIg+41TZfuFcY3z7lIuG6solmIgoMW9zVlkh/wz25T1JBfDdnNQWFR+dyYzICPlXIyXF7+YOQYIY6QcveDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:12.612149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3825","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb9168b81c4c1bcf9ddccc107816729d4fad241d5eec61cb60cac2faeccd910f","sha256:b84c4372c0affa88f8ecb978bb83748163eb70748686d65e5aaa933d6d4594d7"],"state_sha256":"3f0d5f330c18d1b6c0855294b3d343b72b89e704dad504e0de80be76b3c32c58"}