{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5NQXOPJ4WC3W33EV2IUNFYCZJ7","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":"f27c31239a49d940ea27ea8484cc603d6dc71ba891ad9a9a877f78c5a33a5f68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-06-11T21:06:43Z","title_canon_sha256":"b191892453ffcfe1b4743745d2c29ce131d3faad1f4cf587c262c2e85890e627"},"schema_version":"1.0","source":{"id":"1506.03838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03838","created_at":"2026-05-18T01:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03838v1","created_at":"2026-05-18T01:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03838","created_at":"2026-05-18T01:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"5NQXOPJ4WC3W","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5NQXOPJ4WC3W33EV","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5NQXOPJ4","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:200acc01083716a616d21d42243a64758cfae4084fee584ad28137dfad9022ae","target":"graph","created_at":"2026-05-18T01:51:49Z","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 show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.","authors_text":"Gerhard J. Woeginger, Jiehua Chen, Kirk Pruhs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-06-11T21:06:43Z","title":"The one-dimensional Euclidean domain: Finitely many obstructions are not enough"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03838","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:ad60954016f15607686e9ae5955ddb922e684fae07c4de1afe425781206c9753","target":"record","created_at":"2026-05-18T01:51:49Z","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":"f27c31239a49d940ea27ea8484cc603d6dc71ba891ad9a9a877f78c5a33a5f68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-06-11T21:06:43Z","title_canon_sha256":"b191892453ffcfe1b4743745d2c29ce131d3faad1f4cf587c262c2e85890e627"},"schema_version":"1.0","source":{"id":"1506.03838","kind":"arxiv","version":1}},"canonical_sha256":"eb61773d3cb0b76dec95d228d2e0594fc98504c07597a80d3451427774e1b3f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb61773d3cb0b76dec95d228d2e0594fc98504c07597a80d3451427774e1b3f3","first_computed_at":"2026-05-18T01:51:49.094092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:49.094092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BBD6Px9KhZBCwm7UqnIAeJAE3qpsldEmEJZR4mVLWlgzXuz5PwcUhK/9VK2+vryaUeOVqqODRr/oYT/zixMZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:49.094830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad60954016f15607686e9ae5955ddb922e684fae07c4de1afe425781206c9753","sha256:200acc01083716a616d21d42243a64758cfae4084fee584ad28137dfad9022ae"],"state_sha256":"27f35ff36bcc3d1c0164679cbd7a2d2be9d18f6000f42a189b1f85d5913a9581"}