{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7VMHTIJETAQ4PMLRMMJLLTJKV7","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":"77a6289ac0ebeb4d3a46de58fb6232c296ac368260dd927ba5b71341d669237a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-04-27T09:33:44Z","title_canon_sha256":"e1afc99c81ac0795f1d424c1eb077c44dd91a376fbd6dae9a60a07dfcbfb2b7f"},"schema_version":"1.0","source":{"id":"0904.4119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4119","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4119v2","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4119","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"7VMHTIJETAQ4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7VMHTIJETAQ4PMLR","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7VMHTIJE","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:01c3a2e764891ec956b7593af04a937af6dcecb5d75a13239faa00206dcb8176","target":"graph","created_at":"2026-05-18T01:37:40Z","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 a temporal logic EF+F^-1 for unranked, unordered finite trees. The logic has two operators: EF\\phi, which says \"in some proper descendant \\phi holds\", and F^-1\\phi, which says \"in some proper ancestor \\phi holds\". We present an algorithm for deciding if a regular language of unranked finite trees can be expressed in EF+F^-1. The algorithm uses a characterization expressed in terms of forest algebras.","authors_text":"Mikolaj Bojanczyk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-04-27T09:33:44Z","title":"Two-Way Unary Temporal Logic over Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4119","kind":"arxiv","version":2},"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":"sha256:56df4bcbe7e0eaabf5ed3efa7224ce84b965a8b983992b2a8206e99c68ec15a6","target":"record","created_at":"2026-05-18T01:37:40Z","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":"77a6289ac0ebeb4d3a46de58fb6232c296ac368260dd927ba5b71341d669237a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-04-27T09:33:44Z","title_canon_sha256":"e1afc99c81ac0795f1d424c1eb077c44dd91a376fbd6dae9a60a07dfcbfb2b7f"},"schema_version":"1.0","source":{"id":"0904.4119","kind":"arxiv","version":2}},"canonical_sha256":"fd5879a1249821c7b1716312b5cd2aaff9249522e9c1a8724266a9b22f961c84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd5879a1249821c7b1716312b5cd2aaff9249522e9c1a8724266a9b22f961c84","first_computed_at":"2026-05-18T01:37:40.428491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:40.428491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ONWVLJ/iKkDZNG4ZwK9G7alQ2Wexcz0FqqwOLj5ak3EA+cd8B+Nf8y4lrob7xY0teV71cr77dWCd7eBR6qBCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:40.429165Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56df4bcbe7e0eaabf5ed3efa7224ce84b965a8b983992b2a8206e99c68ec15a6","sha256:01c3a2e764891ec956b7593af04a937af6dcecb5d75a13239faa00206dcb8176"],"state_sha256":"bb81549663962d61bac82546d908356617bf39887754f001175cbb5f3f6b53a3"}