{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:H6AM4M4ESG6QV4OE53DES5IEUG","short_pith_number":"pith:H6AM4M4E","schema_version":"1.0","canonical_sha256":"3f80ce338491bd0af1c4eec6497504a1b4cf259acfe7a50f1a51e6f6f12801d6","source":{"kind":"arxiv","id":"1510.00596","version":1},"attestation_state":"computed","paper":{"title":"Length of an intersection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Christian Delhomm\\'e, Maurice Pouzet","submitted_at":"2015-09-30T20:45:09Z","abstract_excerpt":"A poset $\\bfp$ is well-partially ordered (WPO) if all its linear extensions are well orders~; the supremum of ordered types of these linear extensions is the {\\em length}, $\\ell(\\bfp)$ of $\\bfp$. We prove that if the vertex set $X$ of $\\bfp$ is infinite, of cardinality $\\kappa$, and the ordering $\\leq$ is the intersection of finitely many partial orderings $\\leq_i$ on $X$, $1\\leq i\\leq n$,\n  then, letting $\\ell(X,\\leq_i)=\\kappa\\multordby q_i+r_i$, with $r_i<\\kappa$, denote the euclidian division by $\\kappa$ (seen as an initial ordinal) of the length of the corresponding poset~:\\[ \\ell(\\bfp)< \\"},"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":"1510.00596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-30T20:45:09Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"96ab1f0f6f94c96cc6b34a8d5183880513b8774342a8694861b8b313bf778699","abstract_canon_sha256":"3c9a2d12bd938479f1dae43c88ba71be1c83b82377807fb600f0dd1832ada5f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:12.542928Z","signature_b64":"u/6ISvm7uhv8Ze2VhcORD2Cpuq5F+Ci76p1QKgeZUVwKhzS/OtPJ4rcrNzCtg6aIJtGelOrj9vNVX9EHR/5hDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f80ce338491bd0af1c4eec6497504a1b4cf259acfe7a50f1a51e6f6f12801d6","last_reissued_at":"2026-05-18T01:31:12.542202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:12.542202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Length of an intersection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Christian Delhomm\\'e, Maurice Pouzet","submitted_at":"2015-09-30T20:45:09Z","abstract_excerpt":"A poset $\\bfp$ is well-partially ordered (WPO) if all its linear extensions are well orders~; the supremum of ordered types of these linear extensions is the {\\em length}, $\\ell(\\bfp)$ of $\\bfp$. We prove that if the vertex set $X$ of $\\bfp$ is infinite, of cardinality $\\kappa$, and the ordering $\\leq$ is the intersection of finitely many partial orderings $\\leq_i$ on $X$, $1\\leq i\\leq n$,\n  then, letting $\\ell(X,\\leq_i)=\\kappa\\multordby q_i+r_i$, with $r_i<\\kappa$, denote the euclidian division by $\\kappa$ (seen as an initial ordinal) of the length of the corresponding poset~:\\[ \\ell(\\bfp)< \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00596","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.00596","created_at":"2026-05-18T01:31:12.542327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.00596v1","created_at":"2026-05-18T01:31:12.542327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00596","created_at":"2026-05-18T01:31:12.542327+00:00"},{"alias_kind":"pith_short_12","alias_value":"H6AM4M4ESG6Q","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"H6AM4M4ESG6QV4OE","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"H6AM4M4E","created_at":"2026-05-18T12:29:22.688609+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/H6AM4M4ESG6QV4OE53DES5IEUG","json":"https://pith.science/pith/H6AM4M4ESG6QV4OE53DES5IEUG.json","graph_json":"https://pith.science/api/pith-number/H6AM4M4ESG6QV4OE53DES5IEUG/graph.json","events_json":"https://pith.science/api/pith-number/H6AM4M4ESG6QV4OE53DES5IEUG/events.json","paper":"https://pith.science/paper/H6AM4M4E"},"agent_actions":{"view_html":"https://pith.science/pith/H6AM4M4ESG6QV4OE53DES5IEUG","download_json":"https://pith.science/pith/H6AM4M4ESG6QV4OE53DES5IEUG.json","view_paper":"https://pith.science/paper/H6AM4M4E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.00596&json=true","fetch_graph":"https://pith.science/api/pith-number/H6AM4M4ESG6QV4OE53DES5IEUG/graph.json","fetch_events":"https://pith.science/api/pith-number/H6AM4M4ESG6QV4OE53DES5IEUG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H6AM4M4ESG6QV4OE53DES5IEUG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H6AM4M4ESG6QV4OE53DES5IEUG/action/storage_attestation","attest_author":"https://pith.science/pith/H6AM4M4ESG6QV4OE53DES5IEUG/action/author_attestation","sign_citation":"https://pith.science/pith/H6AM4M4ESG6QV4OE53DES5IEUG/action/citation_signature","submit_replication":"https://pith.science/pith/H6AM4M4ESG6QV4OE53DES5IEUG/action/replication_record"}},"created_at":"2026-05-18T01:31:12.542327+00:00","updated_at":"2026-05-18T01:31:12.542327+00:00"}