{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3PSBATG4MOKBBNLTAY42I6V36A","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":"08ec59212c09f8249bdc68c3a374f53cb89cfe5146486ee5a7b83adf4d068c92","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-01-10T16:40:19Z","title_canon_sha256":"8e9e6674f7ef040213357f9787318cff0eb404fe9cde420c4f46e8262e93f570"},"schema_version":"1.0","source":{"id":"1701.02673","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02673","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02673v3","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02673","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"pith_short_12","alias_value":"3PSBATG4MOKB","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3PSBATG4MOKBBNLT","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3PSBATG4","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:38405c0bdbb921e7ac0488944e3d1f1b0edf4a3d1ffa7c2a50c57c940f910805","target":"graph","created_at":"2026-05-18T00:52:58Z","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":"First-order logic (FO) over words is shown to be equiexpressive with FO equipped with a restricted set of numerical predicates, namely the order, a binary predicate MSB$_0$, and the finite-degree predicates: FO[Arb] = FO[<, MSB$_0$, Fin].\n  The Crane Beach Property (CBP), introduced more than a decade ago, is true of a logic if all the expressible languages admitting a neutral letter are regular.\n  Although it is known that FO[Arb] does not have the CBP, it is shown here that the (strong form of the) CBP holds for both FO[<, Fin] and FO[<, MSB$_0$]. Thus FO[<, Fin] exhibits a form of locality ","authors_text":"Charles Paperman, Micha\\\"el Cadilhac","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-01-10T16:40:19Z","title":"A Crevice on the Crane Beach: Finite-Degree Predicates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02673","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":"sha256:0383b43c24e2a2244024f1b54d9a0aa199b8006f9837aa86444b75a0e989a76d","target":"record","created_at":"2026-05-18T00:52:58Z","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":"08ec59212c09f8249bdc68c3a374f53cb89cfe5146486ee5a7b83adf4d068c92","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-01-10T16:40:19Z","title_canon_sha256":"8e9e6674f7ef040213357f9787318cff0eb404fe9cde420c4f46e8262e93f570"},"schema_version":"1.0","source":{"id":"1701.02673","kind":"arxiv","version":3}},"canonical_sha256":"dbe4104cdc639410b5730639a47abbf001916ce73e6ae0c27eeeaeff8bc1e39e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbe4104cdc639410b5730639a47abbf001916ce73e6ae0c27eeeaeff8bc1e39e","first_computed_at":"2026-05-18T00:52:58.325167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:58.325167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XZf3nbb6LGmCyqqo+pPJUUu+tel+qgNGiv8dGlWCnSHhiqy5wDOg2DVJexjkIpO1V6YN0mt4k7vart7/KgZhDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:58.325568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02673","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0383b43c24e2a2244024f1b54d9a0aa199b8006f9837aa86444b75a0e989a76d","sha256:38405c0bdbb921e7ac0488944e3d1f1b0edf4a3d1ffa7c2a50c57c940f910805"],"state_sha256":"e48c601a96eb6f1393971935dc9c46f3af6e1691a3266144626f92479a08bdef"}