{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NDQJJWH7RTWWQGS53ABMPO6LB3","short_pith_number":"pith:NDQJJWH7","canonical_record":{"source":{"id":"1409.0731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-02T14:40:43Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"5718064ecd63180edec58a953af6cb0d3a8c34fe5fcb43f228a21d5f5423a702","abstract_canon_sha256":"618fd743dda0fae8c5c3d452a6565a088322b3e14cd7da9aacbb50f54e424b7f"},"schema_version":"1.0"},"canonical_sha256":"68e094d8ff8ced681a5dd802c7bbcb0edbf350d477b6d24e3c9bd7f7caf6e7e6","source":{"kind":"arxiv","id":"1409.0731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0731","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0731v1","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0731","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"pith_short_12","alias_value":"NDQJJWH7RTWW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NDQJJWH7RTWWQGS5","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NDQJJWH7","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NDQJJWH7RTWWQGS53ABMPO6LB3","target":"record","payload":{"canonical_record":{"source":{"id":"1409.0731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-02T14:40:43Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"5718064ecd63180edec58a953af6cb0d3a8c34fe5fcb43f228a21d5f5423a702","abstract_canon_sha256":"618fd743dda0fae8c5c3d452a6565a088322b3e14cd7da9aacbb50f54e424b7f"},"schema_version":"1.0"},"canonical_sha256":"68e094d8ff8ced681a5dd802c7bbcb0edbf350d477b6d24e3c9bd7f7caf6e7e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:46.240592Z","signature_b64":"E56G+cPwjM0/GUqTx0YZ1SY4HzAc6cr8If04dwB9uwh2ALQWZib7yJGypB6G4+6WEqt+GcdBptvddDKcGAn+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68e094d8ff8ced681a5dd802c7bbcb0edbf350d477b6d24e3c9bd7f7caf6e7e6","last_reissued_at":"2026-05-18T02:43:46.240148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:46.240148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.0731","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JLh/eGOsDjP42V4VXvav+IEKJJm4TPRybeo2q7Xm4Pb5ECjl3SVMMjeJDEp/hzN8y0M0wZSFLCRhwYSGqXMGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:52:58.381923Z"},"content_sha256":"51e7991fea3c3011da3b438d3d509d336cf1880e30b335d8e399d447dfa3b9ca","schema_version":"1.0","event_id":"sha256:51e7991fea3c3011da3b438d3d509d336cf1880e30b335d8e399d447dfa3b9ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NDQJJWH7RTWWQGS53ABMPO6LB3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity and Expressivity of Uniform One-Dimensional Fragment with Equality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Antti Kuusisto, Emanuel Kiero\\'nski","submitted_at":"2014-09-02T14:40:43Z","abstract_excerpt":"Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified formula. The fragment is closed under Boolean operations, but additional restrictions (called uniformity conditions) apply to combinations of atomic formulas with two or more variables. The fragment can be seen as a canonical generalization of two-variable logic, defined in order to be able to deal with relations of arbitrary arities. The fragment was introd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0731","kind":"arxiv","version":1},"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":"2026-05-18T02:43:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DWCwsjq7/fna750phn45OkEsP0kGfu+Zl5WABzvIRFmZR+sFyYubWXkpcpmW99Eb+Nv8hqKTEtd0sY9DxedsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:52:58.382521Z"},"content_sha256":"08dbebbae4c477c7484c789043d34a40b655a831a04592940dbf190c994f8783","schema_version":"1.0","event_id":"sha256:08dbebbae4c477c7484c789043d34a40b655a831a04592940dbf190c994f8783"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDQJJWH7RTWWQGS53ABMPO6LB3/bundle.json","state_url":"https://pith.science/pith/NDQJJWH7RTWWQGS53ABMPO6LB3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDQJJWH7RTWWQGS53ABMPO6LB3/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":"2026-05-25T16:52:58Z","links":{"resolver":"https://pith.science/pith/NDQJJWH7RTWWQGS53ABMPO6LB3","bundle":"https://pith.science/pith/NDQJJWH7RTWWQGS53ABMPO6LB3/bundle.json","state":"https://pith.science/pith/NDQJJWH7RTWWQGS53ABMPO6LB3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDQJJWH7RTWWQGS53ABMPO6LB3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NDQJJWH7RTWWQGS53ABMPO6LB3","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":"618fd743dda0fae8c5c3d452a6565a088322b3e14cd7da9aacbb50f54e424b7f","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-02T14:40:43Z","title_canon_sha256":"5718064ecd63180edec58a953af6cb0d3a8c34fe5fcb43f228a21d5f5423a702"},"schema_version":"1.0","source":{"id":"1409.0731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0731","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0731v1","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0731","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"pith_short_12","alias_value":"NDQJJWH7RTWW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NDQJJWH7RTWWQGS5","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NDQJJWH7","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:08dbebbae4c477c7484c789043d34a40b655a831a04592940dbf190c994f8783","target":"graph","created_at":"2026-05-18T02:43:46Z","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":"Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified formula. The fragment is closed under Boolean operations, but additional restrictions (called uniformity conditions) apply to combinations of atomic formulas with two or more variables. The fragment can be seen as a canonical generalization of two-variable logic, defined in order to be able to deal with relations of arbitrary arities. The fragment was introd","authors_text":"Antti Kuusisto, Emanuel Kiero\\'nski","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-02T14:40:43Z","title":"Complexity and Expressivity of Uniform One-Dimensional Fragment with Equality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0731","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":"sha256:51e7991fea3c3011da3b438d3d509d336cf1880e30b335d8e399d447dfa3b9ca","target":"record","created_at":"2026-05-18T02:43:46Z","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":"618fd743dda0fae8c5c3d452a6565a088322b3e14cd7da9aacbb50f54e424b7f","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-09-02T14:40:43Z","title_canon_sha256":"5718064ecd63180edec58a953af6cb0d3a8c34fe5fcb43f228a21d5f5423a702"},"schema_version":"1.0","source":{"id":"1409.0731","kind":"arxiv","version":1}},"canonical_sha256":"68e094d8ff8ced681a5dd802c7bbcb0edbf350d477b6d24e3c9bd7f7caf6e7e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68e094d8ff8ced681a5dd802c7bbcb0edbf350d477b6d24e3c9bd7f7caf6e7e6","first_computed_at":"2026-05-18T02:43:46.240148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:46.240148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E56G+cPwjM0/GUqTx0YZ1SY4HzAc6cr8If04dwB9uwh2ALQWZib7yJGypB6G4+6WEqt+GcdBptvddDKcGAn+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:46.240592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51e7991fea3c3011da3b438d3d509d336cf1880e30b335d8e399d447dfa3b9ca","sha256:08dbebbae4c477c7484c789043d34a40b655a831a04592940dbf190c994f8783"],"state_sha256":"e0088f6d9af87eeed2c5c564220464f6198390cb8f7d5f26bfcd821a17c43150"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCB6/Qi11W3g6nDBh+s+uhAosdUxKDS0ojvDsBX8QJ+3N3eTeWBulXK83HnBf60FQItQs6Ogt/tyOsu41KJcDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:52:58.385896Z","bundle_sha256":"c83185c9ee9ba542c77c7be1f784b425ddc9c5ac3a5232a8e734f4f460deb06d"}}