{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YIAV7LZMOT72QHXIHXDHG4MNWX","short_pith_number":"pith:YIAV7LZM","schema_version":"1.0","canonical_sha256":"c2015faf2c74ffa81ee83dc673718db5ecb6850afde82af40966234a6ae9a244","source":{"kind":"arxiv","id":"1404.2239","version":1},"attestation_state":"computed","paper":{"title":"The linear refinement number and selection theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Boaz Tsaban, Micha{\\l} Machura, Saharon Shelah","submitted_at":"2014-04-08T18:03:36Z","abstract_excerpt":"The \\emph{linear refinement number} $\\mathfrak{lr}$ is the minimal cardinality of a centered family in $[\\omega]^\\omega$ such that no linearly ordered set in $([\\omega]^\\omega,\\subseteq^*)$ refines this family. The \\emph{linear excluded middle number} $\\mathfrak{lx}$ is a variation of $\\mathfrak{lr}$. We show that these numbers estimate the critical cardinalities of a number of selective covering properties. We compare these numbers to the classic combinatorial cardinal characteristics of the continuum. We prove that $\\mathfrak{lr}=\\mathfrak{lx}=\\mathfrak{fd}$ in all models where the continuum"},"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":"1404.2239","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-04-08T18:03:36Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"a201dd1a0da16385f6879dc32edc8a3236fb0e73966c23a0919cd593771f64e4","abstract_canon_sha256":"6858b68870abf914c38671f8abbe2c4eafac2cd4a7ff6b30fe24c425fd64a2b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:59.189466Z","signature_b64":"0vSSv61ukivYPoVQY6BOQDdsK7tUlTc+2YD75GkmD0f6e/A0eTKi+bsw0d4Pt5Z/0f6JFJQbbGa1sCtnwjMfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2015faf2c74ffa81ee83dc673718db5ecb6850afde82af40966234a6ae9a244","last_reissued_at":"2026-05-18T01:15:59.188823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:59.188823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The linear refinement number and selection theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Boaz Tsaban, Micha{\\l} Machura, Saharon Shelah","submitted_at":"2014-04-08T18:03:36Z","abstract_excerpt":"The \\emph{linear refinement number} $\\mathfrak{lr}$ is the minimal cardinality of a centered family in $[\\omega]^\\omega$ such that no linearly ordered set in $([\\omega]^\\omega,\\subseteq^*)$ refines this family. The \\emph{linear excluded middle number} $\\mathfrak{lx}$ is a variation of $\\mathfrak{lr}$. We show that these numbers estimate the critical cardinalities of a number of selective covering properties. We compare these numbers to the classic combinatorial cardinal characteristics of the continuum. We prove that $\\mathfrak{lr}=\\mathfrak{lx}=\\mathfrak{fd}$ in all models where the continuum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2239","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":"1404.2239","created_at":"2026-05-18T01:15:59.188922+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2239v1","created_at":"2026-05-18T01:15:59.188922+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2239","created_at":"2026-05-18T01:15:59.188922+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIAV7LZMOT72","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIAV7LZMOT72QHXI","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIAV7LZM","created_at":"2026-05-18T12:28:57.508820+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/YIAV7LZMOT72QHXIHXDHG4MNWX","json":"https://pith.science/pith/YIAV7LZMOT72QHXIHXDHG4MNWX.json","graph_json":"https://pith.science/api/pith-number/YIAV7LZMOT72QHXIHXDHG4MNWX/graph.json","events_json":"https://pith.science/api/pith-number/YIAV7LZMOT72QHXIHXDHG4MNWX/events.json","paper":"https://pith.science/paper/YIAV7LZM"},"agent_actions":{"view_html":"https://pith.science/pith/YIAV7LZMOT72QHXIHXDHG4MNWX","download_json":"https://pith.science/pith/YIAV7LZMOT72QHXIHXDHG4MNWX.json","view_paper":"https://pith.science/paper/YIAV7LZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2239&json=true","fetch_graph":"https://pith.science/api/pith-number/YIAV7LZMOT72QHXIHXDHG4MNWX/graph.json","fetch_events":"https://pith.science/api/pith-number/YIAV7LZMOT72QHXIHXDHG4MNWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIAV7LZMOT72QHXIHXDHG4MNWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIAV7LZMOT72QHXIHXDHG4MNWX/action/storage_attestation","attest_author":"https://pith.science/pith/YIAV7LZMOT72QHXIHXDHG4MNWX/action/author_attestation","sign_citation":"https://pith.science/pith/YIAV7LZMOT72QHXIHXDHG4MNWX/action/citation_signature","submit_replication":"https://pith.science/pith/YIAV7LZMOT72QHXIHXDHG4MNWX/action/replication_record"}},"created_at":"2026-05-18T01:15:59.188922+00:00","updated_at":"2026-05-18T01:15:59.188922+00:00"}