{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:A4PXXUP3XIDQR3E7XTWFR67ITO","short_pith_number":"pith:A4PXXUP3","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"},"canonical_sha256":"071f7bd1fbba0708ec9fbcec58fbe89b847b768847930a46d54ca07921d42451","source":{"kind":"arxiv","id":"1905.04756","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04756","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04756v1","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04756","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"A4PXXUP3XIDQ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"A4PXXUP3XIDQR3E7","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"A4PXXUP3","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:A4PXXUP3XIDQR3E7XTWFR67ITO","target":"record","payload":{"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"},"canonical_sha256":"071f7bd1fbba0708ec9fbcec58fbe89b847b768847930a46d54ca07921d42451","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"},"source_kind":"arxiv","source_id":"1905.04756","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"krFPS3/yhFaIUXuf1llzciP9czIEHxCTsdyZ5P+ImiqXRiqjAJ+fxn4o/wcKJRt2anXggxL6dQlcBdbpg8n1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:42:06.215456Z"},"content_sha256":"fdf12e5e772c84dc0a3401baf3ef33dc4d8c13406c31e31822d06efa02a61de4","schema_version":"1.0","event_id":"sha256:fdf12e5e772c84dc0a3401baf3ef33dc4d8c13406c31e31822d06efa02a61de4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:A4PXXUP3XIDQR3E7XTWFR67ITO","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kt3gvNtzWfBHGqhJZE73rZUhLLMCuYVx8prB86PdeCHPKPYb33NnPNJEnTBO+uvvdjf8eZPPVlofyMl8aiC8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:42:06.215968Z"},"content_sha256":"b602d313033a523d551fcdf31b9f5ec84bd8bc460a5ff896d6ff252c0190eaf8","schema_version":"1.0","event_id":"sha256:b602d313033a523d551fcdf31b9f5ec84bd8bc460a5ff896d6ff252c0190eaf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/bundle.json","state_url":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T08:42:06Z","links":{"resolver":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO","bundle":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/bundle.json","state":"https://pith.science/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4PXXUP3XIDQR3E7XTWFR67ITO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:A4PXXUP3XIDQR3E7XTWFR67ITO","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":"21a95c5bf2b1bdfa558b13929ec03fa6ce10cb86423fea46a8c2d0bc4c9b2f51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-12T17:57:10Z","title_canon_sha256":"90b741ca6dd2276dab16b4492d7d7dd85b6dec006467d94158a2af88b86cab2d"},"schema_version":"1.0","source":{"id":"1905.04756","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04756","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04756v1","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04756","created_at":"2026-05-17T23:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"A4PXXUP3XIDQ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"A4PXXUP3XIDQR3E7","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"A4PXXUP3","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:b602d313033a523d551fcdf31b9f5ec84bd8bc460a5ff896d6ff252c0190eaf8","target":"graph","created_at":"2026-05-17T23:46:23Z","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 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.","authors_text":"J\\\"org Brendle, Vera Fischer, Yurii Khomskii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-12T17:57:10Z","title":"Definable Maximal Independent Families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04756","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:fdf12e5e772c84dc0a3401baf3ef33dc4d8c13406c31e31822d06efa02a61de4","target":"record","created_at":"2026-05-17T23:46:23Z","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":"21a95c5bf2b1bdfa558b13929ec03fa6ce10cb86423fea46a8c2d0bc4c9b2f51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-12T17:57:10Z","title_canon_sha256":"90b741ca6dd2276dab16b4492d7d7dd85b6dec006467d94158a2af88b86cab2d"},"schema_version":"1.0","source":{"id":"1905.04756","kind":"arxiv","version":1}},"canonical_sha256":"071f7bd1fbba0708ec9fbcec58fbe89b847b768847930a46d54ca07921d42451","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"071f7bd1fbba0708ec9fbcec58fbe89b847b768847930a46d54ca07921d42451","first_computed_at":"2026-05-17T23:46:23.640580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:23.640580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wv8jPGbFHOW/xGw2UUJuxxg5KmdNWDsywSsIjv7O9SjgnIva6KdcmavpzfUwFzxJDz5R2lMiYaVDp45lz3zGCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:23.641181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.04756","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdf12e5e772c84dc0a3401baf3ef33dc4d8c13406c31e31822d06efa02a61de4","sha256:b602d313033a523d551fcdf31b9f5ec84bd8bc460a5ff896d6ff252c0190eaf8"],"state_sha256":"73f9e7f869ae83ccff3ef9b3585703574621dda2f19ea5b4f236bf1348734c90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKOVISxYhncNVq/YYHsxFqRHEHEdOSIjYB43GlTzmMyZ/nmehdaHfJKTMQQ0iUQIUgUpwtyDTGCyRwLhrj3ACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:42:06.218590Z","bundle_sha256":"d2a8ff9635ba68a8f9ffb6f147bcf7d9a4b11d06f78578694962031effe64863"}}