{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KEF2OFDCGHTV7OVGHCKFGMOY4X","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":"41b0d8b1a9598aae8989af82c5c54ed84b00d5cb48a75646b9c88f6a63730ad6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-06-10T07:45:53Z","title_canon_sha256":"93729d50de24178eea2462773792237a2ca0b607b49e628f4159912fe05b8046"},"schema_version":"1.0","source":{"id":"1606.03217","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03217","created_at":"2026-05-18T00:20:17Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03217v2","created_at":"2026-05-18T00:20:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03217","created_at":"2026-05-18T00:20:17Z"},{"alias_kind":"pith_short_12","alias_value":"KEF2OFDCGHTV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KEF2OFDCGHTV7OVG","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KEF2OFDC","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:89716522e5af4299b14307c7c0aca2ada351ef41df23dab401db004ee22d3c13","target":"graph","created_at":"2026-05-18T00:20:17Z","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":"Several years ago Th\\'erien and Wilke exhibited a decidable characterization of the languages of words that are definable in FO2(<,+1). Their proof relies on three separate ingredients. The first one is the characterization of the languages that are definable in FO2(<) as those whose syntactic semigroup belongs to the variety DA. Then, this result is combined with a wreath product argument showing that being definable in FO2(<,+1) corresponds to having a syntactic semigroup in DA*D. Finally, proving that membership of a semigroup in DA*D is decidable requires a third ingredient: the \"locality\"","authors_text":"Luc Segoufin, Thomas Place","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-06-10T07:45:53Z","title":"Decidable Characterization of FO2(<,+1) and locality of DA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03217","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:e575bfda9a21da52ae450a88c37348c35c311b54f04302561693261234e8daee","target":"record","created_at":"2026-05-18T00:20:17Z","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":"41b0d8b1a9598aae8989af82c5c54ed84b00d5cb48a75646b9c88f6a63730ad6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-06-10T07:45:53Z","title_canon_sha256":"93729d50de24178eea2462773792237a2ca0b607b49e628f4159912fe05b8046"},"schema_version":"1.0","source":{"id":"1606.03217","kind":"arxiv","version":2}},"canonical_sha256":"510ba7146231e75fbaa638945331d8e5c40a9fc63e45e77abf94702a4f2827ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"510ba7146231e75fbaa638945331d8e5c40a9fc63e45e77abf94702a4f2827ff","first_computed_at":"2026-05-18T00:20:17.824534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:17.824534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QTHrehM7dzZ29HWmn7AT4YZw+k35/G8Nsle2SoS32xGmUfN38J2G3Y0Dk6TFkjclxHdauIGxcKR6PG9WQ9d3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:17.825121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03217","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e575bfda9a21da52ae450a88c37348c35c311b54f04302561693261234e8daee","sha256:89716522e5af4299b14307c7c0aca2ada351ef41df23dab401db004ee22d3c13"],"state_sha256":"31810212ebe911fae41067d7fcb7b4c0986031f2fb6c6af44ed82ee5f0c676b5"}