{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:J6XJGOSU7ZMPV3DNAGYPL2CHES","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":"35f6ff4d952f5a7bf73c0c36c3e72d3ea6c6f55934c7118196d38f8daf6ef9c8","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1993-10-15T00:00:00Z","title_canon_sha256":"48d1d8172d909a1df28426bec72cf2551e3b6c9e7ee5a53674769dc44390c06c"},"schema_version":"1.0","source":{"id":"math/9310224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9310224","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9310224v1","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9310224","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"J6XJGOSU7ZMP","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"J6XJGOSU7ZMPV3DN","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"J6XJGOSU","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:8413881262f8dd31e2581c8b04f3871adfec1195b1795cae7888551c84b856b3","target":"graph","created_at":"2026-05-18T01:05:51Z","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 a model where there is a ccc Souslin forcing which does not satisfy the Knaster condition. Next, we present a model where there is a sigma-linked not sigma-centered Souslin forcing such that all its small subsets are sigma-centered but Martin Axiom fails for this order. Furthermore, we construct a totally nonhomogeneous Souslin forcing and we build a Souslin forcing which is proper but not ccc that does not contain a perfect set of mutually incompatible conditions. Finally we show that ccc Sigma^1_2-notions of forcing may not be indestructible ccc.","authors_text":"Andrzej Ros{\\l}anowski, Haim Judah, Saharon Shelah","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1993-10-15T00:00:00Z","title":"Examples for Souslin forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9310224","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:bc40433f336b8f1b86f2158d47ae79099bed1d140366ac5fcad3dd68bf14cf75","target":"record","created_at":"2026-05-18T01:05:51Z","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":"35f6ff4d952f5a7bf73c0c36c3e72d3ea6c6f55934c7118196d38f8daf6ef9c8","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1993-10-15T00:00:00Z","title_canon_sha256":"48d1d8172d909a1df28426bec72cf2551e3b6c9e7ee5a53674769dc44390c06c"},"schema_version":"1.0","source":{"id":"math/9310224","kind":"arxiv","version":1}},"canonical_sha256":"4fae933a54fe58faec6d01b0f5e84724a67af8a8783be8592d7e31bfc7b2936f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fae933a54fe58faec6d01b0f5e84724a67af8a8783be8592d7e31bfc7b2936f","first_computed_at":"2026-05-18T01:05:51.841991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:51.841991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dxsSa6LHaBLKl4s/HW9IX9+bdVJ48lZLlJET42ZZVf8oDL3oodxY+fe7V0vw51QyK5J7gQzHjAq0P14fJz/TCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:51.842426Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9310224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc40433f336b8f1b86f2158d47ae79099bed1d140366ac5fcad3dd68bf14cf75","sha256:8413881262f8dd31e2581c8b04f3871adfec1195b1795cae7888551c84b856b3"],"state_sha256":"49c96677b115fc4e39a22499dc817209294dcbc803593a8078af7239d01c70f2"}