{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NS5GV5MHLHJNAH6EDR2IOFQGI2","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":"2b04fd10703f2bd67ed511b3dacdcaf6ac87907b9339cad04e827f29ef8dca9d","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-09-10T02:34:04Z","title_canon_sha256":"626bc800bb85595d0e097af517968f17c2bf3eee610bfaf21874ca8ad446f0a3"},"schema_version":"1.0","source":{"id":"1809.03104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03104","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03104v1","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03104","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"NS5GV5MHLHJN","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NS5GV5MHLHJNAH6E","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NS5GV5MH","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:40b0d0ecda6b3b7ec6d4cb451a933bd7ca9cfa0b02e64a39bbae558ada2be7f5","target":"graph","created_at":"2026-05-18T00:06:09Z","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":"We consider the problem of computing the measure of a regular language of infinite binary trees. While the general case remains unsolved, we show that the measure of a language defined by a first-order formula with no descendant  relation or by a Boolean combination of conjunctive queries (with descendant relation) is rational and computable. Additionally, we provide an example of a first-order formula that uses descendant relation and defines a language of infinite trees having an irrational measure.","authors_text":"Marcin Przyby{\\l}ko","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-09-10T02:34:04Z","title":"On Computing the Measures of First-Order Definable Sets of Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03104","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":"sha256:8a5f95cdec4aaf2ca4e183020781368eec29cbd4538dbe5220d72a72981bf108","target":"record","created_at":"2026-05-18T00:06:09Z","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":"2b04fd10703f2bd67ed511b3dacdcaf6ac87907b9339cad04e827f29ef8dca9d","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-09-10T02:34:04Z","title_canon_sha256":"626bc800bb85595d0e097af517968f17c2bf3eee610bfaf21874ca8ad446f0a3"},"schema_version":"1.0","source":{"id":"1809.03104","kind":"arxiv","version":1}},"canonical_sha256":"6cba6af58759d2d01fc41c74871606468cb49a78464de3c2dd5f69707d0cb653","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cba6af58759d2d01fc41c74871606468cb49a78464de3c2dd5f69707d0cb653","first_computed_at":"2026-05-18T00:06:09.998267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:09.998267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RNv58uvp+Knx4BOJngGJWDjw+aM/B6bSiK7MbYDrMv29HvcKrQf5R6tAI7kn8EMnKKKifAiqbra9vhu43X7uDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:09.998815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a5f95cdec4aaf2ca4e183020781368eec29cbd4538dbe5220d72a72981bf108","sha256:40b0d0ecda6b3b7ec6d4cb451a933bd7ca9cfa0b02e64a39bbae558ada2be7f5"],"state_sha256":"06571922ab9784838b3bfd90e72febf20381bbacd02f9f6a0e60290b64fd15ec"}