{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DEEGE46KAJH3WIZSNDZ6CXMNO2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1f0a9a7d652198f01fe77adc32072f17361db1cc3b42b206758401c897df204b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-23T06:33:32Z","title_canon_sha256":"92c91b37b8e7a3583096f14e056b10f1b68bcb2882508487ba1e8b582b7bdff5"},"schema_version":"1.0","source":{"id":"1810.09680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09680","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09680v1","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09680","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"DEEGE46KAJH3","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DEEGE46KAJH3WIZS","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DEEGE46K","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:e45a90075314f6b27dfd8034e0ce7174601a2aabf95cecb9afa184bbe1f1b213","target":"graph","created_at":"2026-05-18T00:02:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Osvaldo Guzman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-23T06:33:32Z","title":"P-points, MAD families and Cardinal Invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09680","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2cdb22f96a75d8dc94b2ac3c1a8e1df0e2d1374f21b078caefdf8eb5beaf17ad","target":"record","created_at":"2026-05-18T00:02:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1f0a9a7d652198f01fe77adc32072f17361db1cc3b42b206758401c897df204b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-23T06:33:32Z","title_canon_sha256":"92c91b37b8e7a3583096f14e056b10f1b68bcb2882508487ba1e8b582b7bdff5"},"schema_version":"1.0","source":{"id":"1810.09680","kind":"arxiv","version":1}},"canonical_sha256":"19086273ca024fbb233268f3e15d8d76937ac0662ff1b5395cdbb3021c0edc15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19086273ca024fbb233268f3e15d8d76937ac0662ff1b5395cdbb3021c0edc15","first_computed_at":"2026-05-18T00:02:29.764374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:29.764374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tySoFoGwLgdc9LT5pgdFB3hmCKbfAL7EiqsN4jX5n5leFEsu1s6SjWD9goptKq760gNs8un0V36daePG4i11BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:29.765024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cdb22f96a75d8dc94b2ac3c1a8e1df0e2d1374f21b078caefdf8eb5beaf17ad","sha256:e45a90075314f6b27dfd8034e0ce7174601a2aabf95cecb9afa184bbe1f1b213"],"state_sha256":"000683de40af8a815deac7c90420d37335860148298da072d6121324320c740b"}