{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DVVS5EYZKO2DHNVVGK2UFD2E4O","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":"690d0879a37bf2e44eda1b103f1b9ced165f3ad0f2dab424098c60134cad1d91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2006-05-02T15:57:08Z","title_canon_sha256":"e7cf1bc2c12ca6c8fce50652032382bd75c39adb47079814a40f1959142e18d6"},"schema_version":"1.0","source":{"id":"math/0605067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605067","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605067v2","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605067","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"pith_short_12","alias_value":"DVVS5EYZKO2D","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DVVS5EYZKO2DHNVV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DVVS5EYZ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:5fc65d9dac913deab48187f15223f68db323c318858504b3987cad8dbb488f2d","target":"graph","created_at":"2026-05-18T03:37:19Z","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 continue investigations of reasonable ultrafilters on uncountable cardinals defined in math.LO/0407498. We introduce stronger properties of ultrafilters and we show that those properties may be handled in lambda-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal lambda with generating system of size less than 2^lambda . We also show how reasonable ultrafilters can be killed by forcing notions which have enough reasonable completeness to be iterated with lambda-supports (and we show th","authors_text":"Andrzej Roslanowski, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2006-05-02T15:57:08Z","title":"Reasonable ultrafilters, again"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605067","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":"sha256:34af4269a481b4a07f7cecec33fe9220e26a93e629a241bccc8ee40d063fd58d","target":"record","created_at":"2026-05-18T03:37:19Z","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":"690d0879a37bf2e44eda1b103f1b9ced165f3ad0f2dab424098c60134cad1d91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2006-05-02T15:57:08Z","title_canon_sha256":"e7cf1bc2c12ca6c8fce50652032382bd75c39adb47079814a40f1959142e18d6"},"schema_version":"1.0","source":{"id":"math/0605067","kind":"arxiv","version":2}},"canonical_sha256":"1d6b2e931953b433b6b532b5428f44e3a5c1170300717a2e382a42abbab81ee6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d6b2e931953b433b6b532b5428f44e3a5c1170300717a2e382a42abbab81ee6","first_computed_at":"2026-05-18T03:37:19.374814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:19.374814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"URcQutfJXKzXyT7pQJJSv1eqI+/vZzU+pRT9EnZpEBYxFK6CqAVTWh5mrFiyGuEymzcufsO0ABBN63TSYl4dAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:19.375197Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34af4269a481b4a07f7cecec33fe9220e26a93e629a241bccc8ee40d063fd58d","sha256:5fc65d9dac913deab48187f15223f68db323c318858504b3987cad8dbb488f2d"],"state_sha256":"329b94ebcc90f9da4623a1ba8dff7f4fc60fd6a0a69b0f3a5cac0822269e745d"}