{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ITNIEOSRXDXLU7OHAETZQTRDTO","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":"80e3144d628ef74a233cf2cc683fd5cfc1db14661135f55871f7a650a0b62fef","cross_cats_sorted":["math.FA","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-07-28T15:44:51Z","title_canon_sha256":"803f8d0f25c791ac8ab1a5ea1ae861a35bf617292c2e5baf87687ded09655957"},"schema_version":"1.0","source":{"id":"1607.08505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08505","created_at":"2026-05-18T00:55:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08505v2","created_at":"2026-05-18T00:55:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08505","created_at":"2026-05-18T00:55:57Z"},{"alias_kind":"pith_short_12","alias_value":"ITNIEOSRXDXL","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"ITNIEOSRXDXLU7OH","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"ITNIEOSR","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:0667f5f2de6f2725bb53f988ca4ae941415c6c7842290a5f2410e12dd483940a","target":"graph","created_at":"2026-05-18T00:55:57Z","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 investigate states on von Neumann algebras which are not normal but enjoy various forms of infinite additivity, and show that these exist on $B(H)$ if and only if the cardinality of an orthonormal basis of $H$ satisfies various large cardinal conditions. For instance, there is a singular countably additive pure state on $B(l^2(\\kappa))$ if and only if $\\kappa$ is Ulam measurable, and there is a singular ${<}\\,\\kappa$-additive pure state on $B(l^2(\\kappa))$ if and only if $\\kappa$ is measurable. The proofs make use of Farah and Weaver's theory of quantum filters. Applications to Ueda's peak ","authors_text":"David P. Blecher, Nik Weaver","cross_cats":["math.FA","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-07-28T15:44:51Z","title":"Quantum measurable cardinals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08505","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":"sha256:00fd227cb0212867c901cba263d444f68d93d0a2caa09e5f27a29583c9e0f8ca","target":"record","created_at":"2026-05-18T00:55:57Z","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":"80e3144d628ef74a233cf2cc683fd5cfc1db14661135f55871f7a650a0b62fef","cross_cats_sorted":["math.FA","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-07-28T15:44:51Z","title_canon_sha256":"803f8d0f25c791ac8ab1a5ea1ae861a35bf617292c2e5baf87687ded09655957"},"schema_version":"1.0","source":{"id":"1607.08505","kind":"arxiv","version":2}},"canonical_sha256":"44da823a51b8eeba7dc70127984e239b9720f20687d1566c6bba13ccef64dec3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44da823a51b8eeba7dc70127984e239b9720f20687d1566c6bba13ccef64dec3","first_computed_at":"2026-05-18T00:55:57.790924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:57.790924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BcZ2qEqA3xLHsBQv+YyWvHUloofiYG3vX7pjxUphaWEjhg2gPLaVQadLuL3NG5VLVnk63GggB3n77Vb3j29FAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:57.791359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00fd227cb0212867c901cba263d444f68d93d0a2caa09e5f27a29583c9e0f8ca","sha256:0667f5f2de6f2725bb53f988ca4ae941415c6c7842290a5f2410e12dd483940a"],"state_sha256":"e1c442603646d59e379fe7905e09df264d6fc2c20fc9e68f0261bd0b64e36efe"}