{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CQZ6NR4VFSOATIPTEPTRINQ72A","short_pith_number":"pith:CQZ6NR4V","schema_version":"1.0","canonical_sha256":"1433e6c7952c9c09a1f323e714361fd01a6677cc6aad3d3454d743041b01be65","source":{"kind":"arxiv","id":"1510.04067","version":2},"attestation_state":"computed","paper":{"title":"Squares and narrow systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Chris Lambie-Hanson","submitted_at":"2015-10-14T12:50:37Z","abstract_excerpt":"A narrow system is a combinatorial object introduced by Magidor and Shelah in connection with work on the tree property at successors of singular cardinals. In analogy to the tree property, a cardinal $\\kappa$ satisfies the \\emph{narrow system property} if every narrow system of height $\\kappa$ has a cofinal branch. In this paper, we study connections between the narrow system property, square principles, and forcing axioms. We prove, assuming large cardinals, both that it is consistent that $\\aleph_{\\omega+1}$ satisfies the narrow system property and $\\square_{\\aleph_{\\omega}, < \\aleph_{\\omeg"},"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":"1510.04067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-14T12:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"63b52196186da0c9255fa2b22ab7efce6125f40ea6678e11041736dbfe73da3e","abstract_canon_sha256":"389b303928bbb834ad8d788d80400a912276feedbdb1e28ef7d1bd72cf3377c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:32.129217Z","signature_b64":"kBJUbz3/w7YaO8AnHgECk2ZC2DzyWiHn/REdJ1IhYsqjyfelhwzXeDuXze53G1JeslRU1pnIDZcyhzjfVLfSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1433e6c7952c9c09a1f323e714361fd01a6677cc6aad3d3454d743041b01be65","last_reissued_at":"2026-05-18T00:46:32.128489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:32.128489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Squares and narrow systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Chris Lambie-Hanson","submitted_at":"2015-10-14T12:50:37Z","abstract_excerpt":"A narrow system is a combinatorial object introduced by Magidor and Shelah in connection with work on the tree property at successors of singular cardinals. In analogy to the tree property, a cardinal $\\kappa$ satisfies the \\emph{narrow system property} if every narrow system of height $\\kappa$ has a cofinal branch. In this paper, we study connections between the narrow system property, square principles, and forcing axioms. We prove, assuming large cardinals, both that it is consistent that $\\aleph_{\\omega+1}$ satisfies the narrow system property and $\\square_{\\aleph_{\\omega}, < \\aleph_{\\omeg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04067","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":""},"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":"1510.04067","created_at":"2026-05-18T00:46:32.128613+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.04067v2","created_at":"2026-05-18T00:46:32.128613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04067","created_at":"2026-05-18T00:46:32.128613+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQZ6NR4VFSOA","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQZ6NR4VFSOATIPT","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQZ6NR4V","created_at":"2026-05-18T12:29:17.054201+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/CQZ6NR4VFSOATIPTEPTRINQ72A","json":"https://pith.science/pith/CQZ6NR4VFSOATIPTEPTRINQ72A.json","graph_json":"https://pith.science/api/pith-number/CQZ6NR4VFSOATIPTEPTRINQ72A/graph.json","events_json":"https://pith.science/api/pith-number/CQZ6NR4VFSOATIPTEPTRINQ72A/events.json","paper":"https://pith.science/paper/CQZ6NR4V"},"agent_actions":{"view_html":"https://pith.science/pith/CQZ6NR4VFSOATIPTEPTRINQ72A","download_json":"https://pith.science/pith/CQZ6NR4VFSOATIPTEPTRINQ72A.json","view_paper":"https://pith.science/paper/CQZ6NR4V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.04067&json=true","fetch_graph":"https://pith.science/api/pith-number/CQZ6NR4VFSOATIPTEPTRINQ72A/graph.json","fetch_events":"https://pith.science/api/pith-number/CQZ6NR4VFSOATIPTEPTRINQ72A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQZ6NR4VFSOATIPTEPTRINQ72A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQZ6NR4VFSOATIPTEPTRINQ72A/action/storage_attestation","attest_author":"https://pith.science/pith/CQZ6NR4VFSOATIPTEPTRINQ72A/action/author_attestation","sign_citation":"https://pith.science/pith/CQZ6NR4VFSOATIPTEPTRINQ72A/action/citation_signature","submit_replication":"https://pith.science/pith/CQZ6NR4VFSOATIPTEPTRINQ72A/action/replication_record"}},"created_at":"2026-05-18T00:46:32.128613+00:00","updated_at":"2026-05-18T00:46:32.128613+00:00"}