{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GYT5ZICPIRKWEJB7KQNIVU3ITD","short_pith_number":"pith:GYT5ZICP","schema_version":"1.0","canonical_sha256":"3627dca04f445562243f541a8ad36898fd9bc8074f9a6f18e89953a193770075","source":{"kind":"arxiv","id":"1803.03583","version":2},"attestation_state":"computed","paper":{"title":"A model with Suslin trees but no minimal uncountable linear orders other than $\\omega_1$ and $-\\omega_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"D\\'aniel T. Soukup","submitted_at":"2018-03-09T16:03:23Z","abstract_excerpt":"We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\\omega_1$ and $-\\omega_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration, proving that one can force CH together with a restricted form of ladder system uniformization on trees, all while preserving a rigid Suslin tree."},"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":"1803.03583","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-09T16:03:23Z","cross_cats_sorted":[],"title_canon_sha256":"ec509f8d8c8abdcaecb616a608af0dfe554ab4d49c727f2d8fd564d578c52401","abstract_canon_sha256":"bba0391e4b0d073fd9ff3de808184f7108112e5296e0dd9ceaa5cdcb82172965"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:33.925233Z","signature_b64":"b5CvsHBkzLtZo2I4LPgPvIxm0G+oJzsJdEBfP7UZ9i0M8+EUKSPBiQYDrh1S8ny4+C4jRugO3gYPPxb9/Ev5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3627dca04f445562243f541a8ad36898fd9bc8074f9a6f18e89953a193770075","last_reissued_at":"2026-05-18T00:21:33.924619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:33.924619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A model with Suslin trees but no minimal uncountable linear orders other than $\\omega_1$ and $-\\omega_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"D\\'aniel T. Soukup","submitted_at":"2018-03-09T16:03:23Z","abstract_excerpt":"We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\\omega_1$ and $-\\omega_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration, proving that one can force CH together with a restricted form of ladder system uniformization on trees, all while preserving a rigid Suslin tree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03583","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":"1803.03583","created_at":"2026-05-18T00:21:33.924702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.03583v2","created_at":"2026-05-18T00:21:33.924702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03583","created_at":"2026-05-18T00:21:33.924702+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/GYT5ZICPIRKWEJB7KQNIVU3ITD","json":"https://pith.science/pith/GYT5ZICPIRKWEJB7KQNIVU3ITD.json","graph_json":"https://pith.science/api/pith-number/GYT5ZICPIRKWEJB7KQNIVU3ITD/graph.json","events_json":"https://pith.science/api/pith-number/GYT5ZICPIRKWEJB7KQNIVU3ITD/events.json","paper":"https://pith.science/paper/GYT5ZICP"},"agent_actions":{"view_html":"https://pith.science/pith/GYT5ZICPIRKWEJB7KQNIVU3ITD","download_json":"https://pith.science/pith/GYT5ZICPIRKWEJB7KQNIVU3ITD.json","view_paper":"https://pith.science/paper/GYT5ZICP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.03583&json=true","fetch_graph":"https://pith.science/api/pith-number/GYT5ZICPIRKWEJB7KQNIVU3ITD/graph.json","fetch_events":"https://pith.science/api/pith-number/GYT5ZICPIRKWEJB7KQNIVU3ITD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GYT5ZICPIRKWEJB7KQNIVU3ITD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GYT5ZICPIRKWEJB7KQNIVU3ITD/action/storage_attestation","attest_author":"https://pith.science/pith/GYT5ZICPIRKWEJB7KQNIVU3ITD/action/author_attestation","sign_citation":"https://pith.science/pith/GYT5ZICPIRKWEJB7KQNIVU3ITD/action/citation_signature","submit_replication":"https://pith.science/pith/GYT5ZICPIRKWEJB7KQNIVU3ITD/action/replication_record"}},"created_at":"2026-05-18T00:21:33.924702+00:00","updated_at":"2026-05-18T00:21:33.924702+00:00"}