{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VLDROFV5MHL2D7VX5TJAVXFZ6V","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":"25dd5c6b6b16f6c26d56bf728c63b0cf7f72e774b4ebfa840ddb778244e38ffb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2024-04-29T14:48:26Z","title_canon_sha256":"d024f556244044120df90807e8806bfbb9a232c20b1797dc76212f6717446bb4"},"schema_version":"1.0","source":{"id":"2404.18749","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.18749","created_at":"2026-07-05T09:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"2404.18749v2","created_at":"2026-07-05T09:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.18749","created_at":"2026-07-05T09:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"VLDROFV5MHL2","created_at":"2026-07-05T09:00:37Z"},{"alias_kind":"pith_short_16","alias_value":"VLDROFV5MHL2D7VX","created_at":"2026-07-05T09:00:37Z"},{"alias_kind":"pith_short_8","alias_value":"VLDROFV5","created_at":"2026-07-05T09:00:37Z"}],"graph_snapshots":[{"event_id":"sha256:b00c0a0ff378760bedb36375a5c3ca7cb4e551ec26d9fa32067fe9226bbe784a","target":"graph","created_at":"2026-07-05T09:00:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.18749/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A left-variable word over an alphabet~$A$ is a word over~$A \\cup \\{\\star\\}$ whose first letter is the distinguished symbol~$\\star$ standing for a placeholder. The Ordered Variable Word theorem ($\\mathsf{OVW}$), also known as Carlson-Simpson's theorem, is a tree partition theorem, stating that for every finite alphabet~$A$ and every finite coloring of the words over~$A$, there exists a word $c_0$ and an infinite sequence of left-variable words $w_1, w_2, \\dots$ such that $\\{ c_0 \\cdot w_1[a_1] \\cdot \\dots \\cdot w_k[a_k] : k \\in \\mathbb{N}, a_1, \\dots, a_k \\in A \\}$ is monochromatic.\n  In this a","authors_text":"Ludovic Levy Patey, Quentin Le Hou\\'erou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2024-04-29T14:48:26Z","title":"$\\Pi^0_4$ conservation of the Ordered Variable Word theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.18749","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":"sha256:991138ce3f428f461803baca83e52783192f3d9fb2ee2c0da6743b7671cc5463","target":"record","created_at":"2026-07-05T09:00:37Z","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":"25dd5c6b6b16f6c26d56bf728c63b0cf7f72e774b4ebfa840ddb778244e38ffb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2024-04-29T14:48:26Z","title_canon_sha256":"d024f556244044120df90807e8806bfbb9a232c20b1797dc76212f6717446bb4"},"schema_version":"1.0","source":{"id":"2404.18749","kind":"arxiv","version":2}},"canonical_sha256":"aac71716bd61d7a1feb7ecd20adcb9f57cc049498d7624553f84d329a546b0f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aac71716bd61d7a1feb7ecd20adcb9f57cc049498d7624553f84d329a546b0f3","first_computed_at":"2026-07-05T09:00:37.074137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:00:37.074137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eun+ZQ3xQvEg7fV52mitKEq9UfyO10+BEaVq9QJz4//+vrzaQWJH3e05sDn8qQmr9BGZVZGOmSjs5SkpAKcIDA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:00:37.074560Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.18749","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:991138ce3f428f461803baca83e52783192f3d9fb2ee2c0da6743b7671cc5463","sha256:b00c0a0ff378760bedb36375a5c3ca7cb4e551ec26d9fa32067fe9226bbe784a"],"state_sha256":"615379313969452f1216a917367bcc65d65bd8b970b96c93dd0bdfd5aa6451b0"}