{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HUPJFV6MUALWCMXEJB5SMLDVIJ","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":"9c99922bae16965cfc771c9132076a86d9632db2902861d5a5b23d64c17b7d09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-04-29T13:03:17Z","title_canon_sha256":"db4ab6c7c1cd2cce81419ae91b03cade2193a08056baa34728edcc166ec43e1b"},"schema_version":"1.0","source":{"id":"1404.7343","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7343","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7343v3","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7343","created_at":"2026-05-18T02:26:45Z"},{"alias_kind":"pith_short_12","alias_value":"HUPJFV6MUALW","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HUPJFV6MUALWCMXE","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HUPJFV6M","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:f24ed33572390559b9b6454e05ffd6710c58a674899b25662255c9a843d0aa23","target":"graph","created_at":"2026-05-18T02:26:45Z","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 answer Question~3.2 from Shelah \\cite{Sh:666}: Given a maximal almost disjoint (mad) family $\\mathcal A$ of size $\\aleph_1$, we construct a forcing ${\\mathbb Q}(\\mathcal A)$ that has Axiom A, is ${}^\\omega \\omega$-bounding, preserves selective ultrafilters, has the $\\aleph_2$-properness isomorphism condition (p.i.c.), and destroys the mad family $\\mathcal A$. We develop a new construction technique for partial orders, combining ladder systems for $\\omega_1$ with trees of normed creatures.\n  Countable support iteration of the new kind of iterands solves Roitman's problem in the case of $d=\\a","authors_text":"Heike Mildenberger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-04-29T13:03:17Z","title":"A solution to Roitman's problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7343","kind":"arxiv","version":3},"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:fab9d0e9ceeb183063e7ca34bce77e49a7936684bc372ed713daa13ea368f80e","target":"record","created_at":"2026-05-18T02:26:45Z","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":"9c99922bae16965cfc771c9132076a86d9632db2902861d5a5b23d64c17b7d09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-04-29T13:03:17Z","title_canon_sha256":"db4ab6c7c1cd2cce81419ae91b03cade2193a08056baa34728edcc166ec43e1b"},"schema_version":"1.0","source":{"id":"1404.7343","kind":"arxiv","version":3}},"canonical_sha256":"3d1e92d7cca0176132e4487b262c75426cd4bad630c16408ca055d043f3168ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d1e92d7cca0176132e4487b262c75426cd4bad630c16408ca055d043f3168ee","first_computed_at":"2026-05-18T02:26:45.463643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:45.463643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N5Xg+HbpY+6d8LEYaLa7o7w6ir9vszBwYciTyjc/MGl+HNDvmkX2fbqROFAfXJcRtO1l2/yO2O9FQiEQgXR4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:45.464024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7343","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fab9d0e9ceeb183063e7ca34bce77e49a7936684bc372ed713daa13ea368f80e","sha256:f24ed33572390559b9b6454e05ffd6710c58a674899b25662255c9a843d0aa23"],"state_sha256":"7f755d30cb16cb3ddd966069e84443114ecad56fcf3c8d4267a80accfec24f26"}