{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AZ5X6KKGW4AFHVS7AR4Z4F2FWD","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":"cd15749f9d42f3b9da0b9faed9af0d1e412673ff18f166af289d764eaf9c0b5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-15T17:18:46Z","title_canon_sha256":"e97e668fdd2d2550a4210dccc72ae311b835aa30164c7a1b38056e540f2ec02e"},"schema_version":"1.0","source":{"id":"1112.3571","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3571","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3571v2","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3571","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"pith_short_12","alias_value":"AZ5X6KKGW4AF","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AZ5X6KKGW4AFHVS7","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AZ5X6KKG","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:23f93e4caad70829f25e360ed2b0ad33a8c390cd4ddbfd0dbad281acb6aa7450","target":"graph","created_at":"2026-05-18T03:40:49Z","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 prove that the statement `For all Borel ideals I and J on $\\omega$, every isomorphism between Boolean algebras $P(\\omega)/I$ and $P(\\omega)/J$ has a continuous representation' is relatively consistent with ZFC. In this model every isomorphism between $P(\\omega)/I$ and any other quotient $P(\\omega)/J$ over a Borel ideal is trivial for a number of Borel ideals I on $\\omega$.\n  We can also assure that the dominating number is equal to $\\aleph_1$ and that $2^{\\aleph_1}>2^{\\aleph_0}$. Therefore the Calkin algebra has outer automorphisms while all automorphisms of $P(\\omega)/Fin$ are trivial.\n  P","authors_text":"Ilijas Farah, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-15T17:18:46Z","title":"Trivial automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3571","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":"sha256:0560b03a4721aedab33078b3ea9b915a715b7bf8e998279d967ce0f3b3446f11","target":"record","created_at":"2026-05-18T03:40:49Z","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":"cd15749f9d42f3b9da0b9faed9af0d1e412673ff18f166af289d764eaf9c0b5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-15T17:18:46Z","title_canon_sha256":"e97e668fdd2d2550a4210dccc72ae311b835aa30164c7a1b38056e540f2ec02e"},"schema_version":"1.0","source":{"id":"1112.3571","kind":"arxiv","version":2}},"canonical_sha256":"067b7f2946b70053d65f04799e1745b0f12d0af6fcff9023c30a2abe513fabf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"067b7f2946b70053d65f04799e1745b0f12d0af6fcff9023c30a2abe513fabf0","first_computed_at":"2026-05-18T03:40:49.535113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:49.535113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bGSr0MX3izK5U1+qmcQcNIGeNYd5Pjqz/wW1Hfa9kajmRMXnnxG3l6U+rKQX8kfkhpAIXfvLqaUAfNKrzOzEBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:49.535799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3571","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0560b03a4721aedab33078b3ea9b915a715b7bf8e998279d967ce0f3b3446f11","sha256:23f93e4caad70829f25e360ed2b0ad33a8c390cd4ddbfd0dbad281acb6aa7450"],"state_sha256":"d723c786ba8a0893dad57897a376ee4c9e790c70da7148eae4ce360d6bf3698c"}