{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JG4HHODUXGAMBQAU7BICGQDHTG","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":"fe935b7737aca798479ad0478beeb25cc3d940c3755a1e082121b373f4c1e2eb","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-11-07T13:35:30Z","title_canon_sha256":"4ca77456ec2e195e0076400d89c6f0bc2249482f6255575ba34aa3c5bddbd3e8"},"schema_version":"1.0","source":{"id":"1311.1677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1677","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1677v2","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1677","created_at":"2026-05-18T02:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"JG4HHODUXGAM","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JG4HHODUXGAMBQAU","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JG4HHODU","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:45345fc4f4363dfbabf053de76447240d0ff7cee738b4185eb2fb360ca7d4e1f","target":"graph","created_at":"2026-05-18T02:41:08Z","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":"We give several topological/combinatorial conditions that, for a filter on $\\omega$, are equivalent to being a non-meager $\\mathsf{P}$-filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a non-meager $\\mathsf{P}$-filter. Here, we identify a filter with a subspace of $2^\\omega$ through characteristic functions. Along the way, we generalize to non-meager $\\mathsf{P}$-filters a result of Miller about $\\mathsf{P}$-points, and we employ and give a new proof of results of Marciszewski. We also employ a theorem of Hern\\'andez-Guti\\'errez and Hru\\v{s}\\'ak, ","authors_text":"Andrea Medini, Kenneth Kunen, Lyubomyr Zdomskyy","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-11-07T13:35:30Z","title":"Seven characterizations of non-meager P-filters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1677","kind":"arxiv","version":2},"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":"sha256:0fbe937c44c1547861553ae5f7a698f271e0952bbce80bc1e15c7c0797b78a81","target":"record","created_at":"2026-05-18T02:41:08Z","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":"fe935b7737aca798479ad0478beeb25cc3d940c3755a1e082121b373f4c1e2eb","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-11-07T13:35:30Z","title_canon_sha256":"4ca77456ec2e195e0076400d89c6f0bc2249482f6255575ba34aa3c5bddbd3e8"},"schema_version":"1.0","source":{"id":"1311.1677","kind":"arxiv","version":2}},"canonical_sha256":"49b873b874b980c0c014f85023406799a28b6f13694c3854692981120b8bd13f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49b873b874b980c0c014f85023406799a28b6f13694c3854692981120b8bd13f","first_computed_at":"2026-05-18T02:41:08.857086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:08.857086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hgiXuP6UbdxSKqbD62ienuUHEAcz+30Q5mFJmbuMMnWszqOdFRM0bPlPaNBwuNfJN20+bc9rn+PG5x9wArnaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:08.857513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fbe937c44c1547861553ae5f7a698f271e0952bbce80bc1e15c7c0797b78a81","sha256:45345fc4f4363dfbabf053de76447240d0ff7cee738b4185eb2fb360ca7d4e1f"],"state_sha256":"db54195664d44018f44f77271a35c2c3058d0ccd59f5d85255701a4029c5d521"}