{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YXTIIFS2ZJ3JQS474ZTN6ELTXD","short_pith_number":"pith:YXTIIFS2","canonical_record":{"source":{"id":"1006.3825","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2010-06-19T00:22:14Z","cross_cats_sorted":[],"title_canon_sha256":"a98403c82fe0377793854bdfa755754b39c4a81eab17bc6ee3a7df8aa5611536","abstract_canon_sha256":"e1c58c021e4fa234cf7349711ceac1993d8bba155bc57ba50e910ac55e12bda2"},"schema_version":"1.0"},"canonical_sha256":"c5e684165aca76984b9fe666df1173b8debc5eb1a16a476fb39d238fa5703b8d","source":{"kind":"arxiv","id":"1006.3825","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YXTIIFS2ZJ3JQS474ZTN6ELTXD","target":"record","payload":{"canonical_record":{"source":{"id":"1006.3825","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2010-06-19T00:22:14Z","cross_cats_sorted":[],"title_canon_sha256":"a98403c82fe0377793854bdfa755754b39c4a81eab17bc6ee3a7df8aa5611536","abstract_canon_sha256":"e1c58c021e4fa234cf7349711ceac1993d8bba155bc57ba50e910ac55e12bda2"},"schema_version":"1.0"},"canonical_sha256":"c5e684165aca76984b9fe666df1173b8debc5eb1a16a476fb39d238fa5703b8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:12.612149Z","signature_b64":"vBkbIg+41TZfuFcY3z7lIuG6solmIgoMW9zVlkh/wz25T1JBfDdnNQWFR+dyYzICPlXIyXF7+YOQYIY6QcveDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5e684165aca76984b9fe666df1173b8debc5eb1a16a476fb39d238fa5703b8d","last_reissued_at":"2026-05-18T03:52:12.611356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:12.611356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.3825","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V5fU3kRamKFBMOBCWcrWox/LicweK348uaQMK60nxtRR8/RkzLeYE6Bow+iqWJ6FT/pFd+XKdbJ2ol4eLoCxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T18:44:25.841837Z"},"content_sha256":"eb9168b81c4c1bcf9ddccc107816729d4fad241d5eec61cb60cac2faeccd910f","schema_version":"1.0","event_id":"sha256:eb9168b81c4c1bcf9ddccc107816729d4fad241d5eec61cb60cac2faeccd910f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YXTIIFS2ZJ3JQS474ZTN6ELTXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parikh's Theorem: A simple and direct automaton construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Javier Esparza, Michael Luttenberger, Pierre Ganty, Stefan Kiefer","submitted_at":"2010-06-19T00:22:14Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3825","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rMMv1ljAsft3zut9Kt3EfB9OS/UL6BqneQv+oOuxx5DGHCfjFimewTwIhvJJeoGajyAZ/U5RFKGC15mJytQFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T18:44:25.842233Z"},"content_sha256":"b84c4372c0affa88f8ecb978bb83748163eb70748686d65e5aaa933d6d4594d7","schema_version":"1.0","event_id":"sha256:b84c4372c0affa88f8ecb978bb83748163eb70748686d65e5aaa933d6d4594d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXTIIFS2ZJ3JQS474ZTN6ELTXD/bundle.json","state_url":"https://pith.science/pith/YXTIIFS2ZJ3JQS474ZTN6ELTXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXTIIFS2ZJ3JQS474ZTN6ELTXD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T18:44:25Z","links":{"resolver":"https://pith.science/pith/YXTIIFS2ZJ3JQS474ZTN6ELTXD","bundle":"https://pith.science/pith/YXTIIFS2ZJ3JQS474ZTN6ELTXD/bundle.json","state":"https://pith.science/pith/YXTIIFS2ZJ3JQS474ZTN6ELTXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXTIIFS2ZJ3JQS474ZTN6ELTXD/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VXF2W3ZtF7FyN/OdNj6npzSex7nQ5mwsLeP0J5GUrrzgELUMrGP5yjFefTK+d5jjr5pD/wVhhrs6Hl+MRyJ3CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T18:44:25.844865Z","bundle_sha256":"81efa12c209de0fd11e38208a5b316196f39caf5c5d07a4b6b6b3d20c2d59298"}}