{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:A4PXXUP3XIDQR3E7XTWFR67ITO","short_pith_number":"pith:A4PXXUP3","schema_version":"1.0","canonical_sha256":"071f7bd1fbba0708ec9fbcec58fbe89b847b768847930a46d54ca07921d42451","source":{"kind":"arxiv","id":"1905.04756","version":1},"attestation_state":"computed","paper":{"title":"Definable Maximal Independent Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"J\\\"org Brendle, Vera Fischer, Yurii Khomskii","submitted_at":"2019-05-12T17:57:10Z","abstract_excerpt":"We study maximal independent families (m.i.f.) in the projective hierarchy. We show that (a) the existence of a $\\boldsymbol{\\Sigma}^1_2$ m.i.f. is equivalent to the existence of a $\\boldsymbol{\\Pi}^1_1$ m.i.f., (b) in the Cohen model, there are no projective maximal independent families, and (c) in the Sacks model, there is a $\\boldsymbol{\\Pi}^1_1$ m.i.f. We also consider a new cardinal invariant related to the question of destroying or preserving maximal independent families."},"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":"1905.04756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-12T17:57:10Z","cross_cats_sorted":[],"title_canon_sha256":"90b741ca6dd2276dab16b4492d7d7dd85b6dec006467d94158a2af88b86cab2d","abstract_canon_sha256":"21a95c5bf2b1bdfa558b13929ec03fa6ce10cb86423fea46a8c2d0bc4c9b2f51"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:23.641181Z","signature_b64":"wv8jPGbFHOW/xGw2UUJuxxg5KmdNWDsywSsIjv7O9SjgnIva6KdcmavpzfUwFzxJDz5R2lMiYaVDp45lz3zGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"071f7bd1fbba0708ec9fbcec58fbe89b847b768847930a46d54ca07921d42451","last_reissued_at":"2026-05-17T23:46:23.640580Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:23.640580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Definable Maximal Independent Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"J\\\"org Brendle, Vera Fischer, Yurii Khomskii","submitted_at":"2019-05-12T17:57:10Z","abstract_excerpt":"We study maximal independent families (m.i.f.) in the projective hierarchy. We show that (a) the existence of a $\\boldsymbol{\\Sigma}^1_2$ m.i.f. is equivalent to the existence of a $\\boldsymbol{\\Pi}^1_1$ m.i.f., (b) in the Cohen model, there are no projective maximal independent families, and (c) in the Sacks model, there is a $\\boldsymbol{\\Pi}^1_1$ m.i.f. We also consider a new cardinal invariant related to the question of destroying or preserving maximal independent families."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04756","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":"1905.04756","created_at":"2026-05-17T23:46:23.640694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.04756v1","created_at":"2026-05-17T23:46:23.640694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04756","created_at":"2026-05-17T23:46:23.640694+00:00"},{"alias_kind":"pith_short_12","alias_value":"A4PXXUP3XIDQ","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"A4PXXUP3XIDQR3E7","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"A4PXXUP3","created_at":"2026-05-18T12:33:12.712433+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/A4PXXUP3XIDQR3E7XTWFR67ITO","json":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO.json","graph_json":"https://pith.science/api/pith-number/A4PXXUP3XIDQR3E7XTWFR67ITO/graph.json","events_json":"https://pith.science/api/pith-number/A4PXXUP3XIDQR3E7XTWFR67ITO/events.json","paper":"https://pith.science/paper/A4PXXUP3"},"agent_actions":{"view_html":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO","download_json":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO.json","view_paper":"https://pith.science/paper/A4PXXUP3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.04756&json=true","fetch_graph":"https://pith.science/api/pith-number/A4PXXUP3XIDQR3E7XTWFR67ITO/graph.json","fetch_events":"https://pith.science/api/pith-number/A4PXXUP3XIDQR3E7XTWFR67ITO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/action/storage_attestation","attest_author":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/action/author_attestation","sign_citation":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/action/citation_signature","submit_replication":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/action/replication_record"}},"created_at":"2026-05-17T23:46:23.640694+00:00","updated_at":"2026-05-17T23:46:23.640694+00:00"}