{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:VLDROFV5MHL2D7VX5TJAVXFZ6V","short_pith_number":"pith:VLDROFV5","schema_version":"1.0","canonical_sha256":"aac71716bd61d7a1feb7ecd20adcb9f57cc049498d7624553f84d329a546b0f3","source":{"kind":"arxiv","id":"2404.18749","version":2},"attestation_state":"computed","paper":{"title":"$\\Pi^0_4$ conservation of the Ordered Variable Word theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ludovic Levy Patey, Quentin Le Hou\\'erou","submitted_at":"2024-04-29T14:48:26Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2404.18749","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2024-04-29T14:48:26Z","cross_cats_sorted":[],"title_canon_sha256":"d024f556244044120df90807e8806bfbb9a232c20b1797dc76212f6717446bb4","abstract_canon_sha256":"25dd5c6b6b16f6c26d56bf728c63b0cf7f72e774b4ebfa840ddb778244e38ffb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:00:37.074560Z","signature_b64":"Eun+ZQ3xQvEg7fV52mitKEq9UfyO10+BEaVq9QJz4//+vrzaQWJH3e05sDn8qQmr9BGZVZGOmSjs5SkpAKcIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aac71716bd61d7a1feb7ecd20adcb9f57cc049498d7624553f84d329a546b0f3","last_reissued_at":"2026-07-05T09:00:37.074137Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:00:37.074137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\Pi^0_4$ conservation of the Ordered Variable Word theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ludovic Levy Patey, Quentin Le Hou\\'erou","submitted_at":"2024-04-29T14:48:26Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.18749","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.18749/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2404.18749","created_at":"2026-07-05T09:00:37.074194+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.18749v2","created_at":"2026-07-05T09:00:37.074194+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.18749","created_at":"2026-07-05T09:00:37.074194+00:00"},{"alias_kind":"pith_short_12","alias_value":"VLDROFV5MHL2","created_at":"2026-07-05T09:00:37.074194+00:00"},{"alias_kind":"pith_short_16","alias_value":"VLDROFV5MHL2D7VX","created_at":"2026-07-05T09:00:37.074194+00:00"},{"alias_kind":"pith_short_8","alias_value":"VLDROFV5","created_at":"2026-07-05T09:00:37.074194+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V","json":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V.json","graph_json":"https://pith.science/api/pith-number/VLDROFV5MHL2D7VX5TJAVXFZ6V/graph.json","events_json":"https://pith.science/api/pith-number/VLDROFV5MHL2D7VX5TJAVXFZ6V/events.json","paper":"https://pith.science/paper/VLDROFV5"},"agent_actions":{"view_html":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V","download_json":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V.json","view_paper":"https://pith.science/paper/VLDROFV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.18749&json=true","fetch_graph":"https://pith.science/api/pith-number/VLDROFV5MHL2D7VX5TJAVXFZ6V/graph.json","fetch_events":"https://pith.science/api/pith-number/VLDROFV5MHL2D7VX5TJAVXFZ6V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V/action/storage_attestation","attest_author":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V/action/author_attestation","sign_citation":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V/action/citation_signature","submit_replication":"https://pith.science/pith/VLDROFV5MHL2D7VX5TJAVXFZ6V/action/replication_record"}},"created_at":"2026-07-05T09:00:37.074194+00:00","updated_at":"2026-07-05T09:00:37.074194+00:00"}