{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DEEGE46KAJH3WIZSNDZ6CXMNO2","short_pith_number":"pith:DEEGE46K","schema_version":"1.0","canonical_sha256":"19086273ca024fbb233268f3e15d8d76937ac0662ff1b5395cdbb3021c0edc15","source":{"kind":"arxiv","id":"1810.09680","version":1},"attestation_state":"computed","paper":{"title":"P-points, MAD families and Cardinal Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Osvaldo Guzman","submitted_at":"2018-10-23T06:33:32Z","abstract_excerpt":"This is the Ph.D. thesis of the author, which was written under the supervision of Michael Hru\\v{s}\\'{a}k at UNAM. The main contributions of this thesis are the following: There is a $+$-Ramsey \\textsf{MAD} family. This answers an old question of Michael Hru\\v{s}\\'{a}k. There are no $P$-points in the Silver model, answering a question of Michael Hru\\v{s}\\'{a}k (this is joint work with David Chodounsk\\'{y}. The statement \\textquotedblleft There are no $P$-points\\textquotedblright\\ is consistent with the continuum being arbitrarily large, this answers an open question regarding $P$-points. Every"},"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":"1810.09680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-23T06:33:32Z","cross_cats_sorted":[],"title_canon_sha256":"92c91b37b8e7a3583096f14e056b10f1b68bcb2882508487ba1e8b582b7bdff5","abstract_canon_sha256":"1f0a9a7d652198f01fe77adc32072f17361db1cc3b42b206758401c897df204b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:29.765024Z","signature_b64":"tySoFoGwLgdc9LT5pgdFB3hmCKbfAL7EiqsN4jX5n5leFEsu1s6SjWD9goptKq760gNs8un0V36daePG4i11BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19086273ca024fbb233268f3e15d8d76937ac0662ff1b5395cdbb3021c0edc15","last_reissued_at":"2026-05-18T00:02:29.764374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:29.764374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"P-points, MAD families and Cardinal Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Osvaldo Guzman","submitted_at":"2018-10-23T06:33:32Z","abstract_excerpt":"This is the Ph.D. thesis of the author, which was written under the supervision of Michael Hru\\v{s}\\'{a}k at UNAM. The main contributions of this thesis are the following: There is a $+$-Ramsey \\textsf{MAD} family. This answers an old question of Michael Hru\\v{s}\\'{a}k. There are no $P$-points in the Silver model, answering a question of Michael Hru\\v{s}\\'{a}k (this is joint work with David Chodounsk\\'{y}. The statement \\textquotedblleft There are no $P$-points\\textquotedblright\\ is consistent with the continuum being arbitrarily large, this answers an open question regarding $P$-points. Every"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09680","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":"1810.09680","created_at":"2026-05-18T00:02:29.764474+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.09680v1","created_at":"2026-05-18T00:02:29.764474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09680","created_at":"2026-05-18T00:02:29.764474+00:00"},{"alias_kind":"pith_short_12","alias_value":"DEEGE46KAJH3","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DEEGE46KAJH3WIZS","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DEEGE46K","created_at":"2026-05-18T12:32:19.392346+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/DEEGE46KAJH3WIZSNDZ6CXMNO2","json":"https://pith.science/pith/DEEGE46KAJH3WIZSNDZ6CXMNO2.json","graph_json":"https://pith.science/api/pith-number/DEEGE46KAJH3WIZSNDZ6CXMNO2/graph.json","events_json":"https://pith.science/api/pith-number/DEEGE46KAJH3WIZSNDZ6CXMNO2/events.json","paper":"https://pith.science/paper/DEEGE46K"},"agent_actions":{"view_html":"https://pith.science/pith/DEEGE46KAJH3WIZSNDZ6CXMNO2","download_json":"https://pith.science/pith/DEEGE46KAJH3WIZSNDZ6CXMNO2.json","view_paper":"https://pith.science/paper/DEEGE46K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.09680&json=true","fetch_graph":"https://pith.science/api/pith-number/DEEGE46KAJH3WIZSNDZ6CXMNO2/graph.json","fetch_events":"https://pith.science/api/pith-number/DEEGE46KAJH3WIZSNDZ6CXMNO2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DEEGE46KAJH3WIZSNDZ6CXMNO2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DEEGE46KAJH3WIZSNDZ6CXMNO2/action/storage_attestation","attest_author":"https://pith.science/pith/DEEGE46KAJH3WIZSNDZ6CXMNO2/action/author_attestation","sign_citation":"https://pith.science/pith/DEEGE46KAJH3WIZSNDZ6CXMNO2/action/citation_signature","submit_replication":"https://pith.science/pith/DEEGE46KAJH3WIZSNDZ6CXMNO2/action/replication_record"}},"created_at":"2026-05-18T00:02:29.764474+00:00","updated_at":"2026-05-18T00:02:29.764474+00:00"}