{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UO5WYODUZVVJT6K232DFC4DSB4","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":"441a89bfb74378cdda8f653148ab49650582031abf7c0556c2af70884505df65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-05T09:45:05Z","title_canon_sha256":"e1f28db2b62aadd60cd320f3b4501725774cc0cae5ee69ea117f37c0cbf2b2d1"},"schema_version":"1.0","source":{"id":"1209.0909","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0909","created_at":"2026-05-18T02:34:52Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0909v3","created_at":"2026-05-18T02:34:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0909","created_at":"2026-05-18T02:34:52Z"},{"alias_kind":"pith_short_12","alias_value":"UO5WYODUZVVJ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UO5WYODUZVVJT6K2","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UO5WYODU","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:8f88aafc649d8cd22fae29d376380dc99535322b07674398f1ef4d3ab6938239","target":"graph","created_at":"2026-05-18T02:34:52Z","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":"A few years ago, Richard Kadison thoroughly analysed the diagonals of projection operators on Hilbert spaces and asked the following question: Let $\\mathcal{A}$ be a masa in a type $II_1$ factor $\\mathcal{M}$ and let $A \\in \\mathcal{A}$ be a positive contraction. Letting $E$ be the canonical normal conditional expectation from $\\mathcal{M}$ to $\\mathcal{A}$, can one find a projection $P \\in \\mathcal{M}$ so that [E(P) = A?] In a later paper, Kadison and Arveson, as an extension, conjectured a Schur-Horn theorem in type $II_1$ factors. In this paper, I give a proof of this conjecture of Arveson ","authors_text":"Mohan Ravichandran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-05T09:45:05Z","title":"The Schur-Horn theorem in von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0909","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:f3e24ddc5f618fb68339fa7014b637df3ef5b7a62b74cc32c774266f694447cc","target":"record","created_at":"2026-05-18T02:34:52Z","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":"441a89bfb74378cdda8f653148ab49650582031abf7c0556c2af70884505df65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-05T09:45:05Z","title_canon_sha256":"e1f28db2b62aadd60cd320f3b4501725774cc0cae5ee69ea117f37c0cbf2b2d1"},"schema_version":"1.0","source":{"id":"1209.0909","kind":"arxiv","version":3}},"canonical_sha256":"a3bb6c3874cd6a99f95ade865170720f21f199cd38c7f02dd6a3c8b7ea9d55a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3bb6c3874cd6a99f95ade865170720f21f199cd38c7f02dd6a3c8b7ea9d55a5","first_computed_at":"2026-05-18T02:34:52.853631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:52.853631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1NcCM3BMzsulyvlFDzKaAIhaOCNba3deOzGuva9AhF1qAxM1Jhfe81wZbvkb9i5r0YWiXFPOmOU93RyaoIpiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:52.854076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0909","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3e24ddc5f618fb68339fa7014b637df3ef5b7a62b74cc32c774266f694447cc","sha256:8f88aafc649d8cd22fae29d376380dc99535322b07674398f1ef4d3ab6938239"],"state_sha256":"c9914d0cb91e49853610c24de89761fab0a07fd36915c49ed104d4ce37b89c29"}