{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OYHTUWS2C36OIEWZIPNKNTDINS","short_pith_number":"pith:OYHTUWS2","canonical_record":{"source":{"id":"1411.4457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-17T12:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"5154b2697cceb62e965853f46195e7b31360c0a488e37e5fec2e896b73108ce3","abstract_canon_sha256":"77968b8168a906c49e3461eca0a1f1002f0d68c0d265b8a171d6bfa89c973218"},"schema_version":"1.0"},"canonical_sha256":"760f3a5a5a16fce412d943daa6cc686ca53f81535427238b7e0dda2ad2099995","source":{"kind":"arxiv","id":"1411.4457","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4457","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4457v1","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4457","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"OYHTUWS2C36O","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OYHTUWS2C36OIEWZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OYHTUWS2","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OYHTUWS2C36OIEWZIPNKNTDINS","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-17T12:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"5154b2697cceb62e965853f46195e7b31360c0a488e37e5fec2e896b73108ce3","abstract_canon_sha256":"77968b8168a906c49e3461eca0a1f1002f0d68c0d265b8a171d6bfa89c973218"},"schema_version":"1.0"},"canonical_sha256":"760f3a5a5a16fce412d943daa6cc686ca53f81535427238b7e0dda2ad2099995","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:28.676701Z","signature_b64":"J/xC0BlW0Q+PDK+rlbKDdDnCvS7ah9Pg+UqM4UuknDYaLgy/kQHnQAAurzbp5VEDqx2/a2blAtAH6ttl/1ReDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"760f3a5a5a16fce412d943daa6cc686ca53f81535427238b7e0dda2ad2099995","last_reissued_at":"2026-05-18T00:44:28.676196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:28.676196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4457","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ITpd6pOlJyCn7aPj2HtNln3StZ2AxEZym3xMAh4RwPYq5Zm734rTBWaUAe/Dx3hZTUBXB28tZed7gai9LQMaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:49:38.890191Z"},"content_sha256":"d9eddb08ddb3bb6d0265d13efc737dca7ac3997b53ada27d51d376249faf815a","schema_version":"1.0","event_id":"sha256:d9eddb08ddb3bb6d0265d13efc737dca7ac3997b53ada27d51d376249faf815a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OYHTUWS2C36OIEWZIPNKNTDINS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariable Schur-Horn theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Mohan Ravichandran, Pedro Massey","submitted_at":"2014-11-17T12:53:25Z","abstract_excerpt":"We prove a variety of results describing the possible diagonals of tuples of commuting hermitian operators in type $II_1$ factors. These results are generalisations of the classical Schur-Horn theorem to the infinite dimensional, multivariable setting. Our description of these possible diagonals uses a natural generalisation of the classical notion of majorization to the multivariable setting. In the special case when both the given tuple and the desired diagonal have finite joint spectrum, our results are complete. When the tuples do not have finite joint spectrum, we are able to prove strong"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4457","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kXP7GOXEycJkKeS68hJR1T8dpV4z2TpZD2UPtN5w+n30OdJdWOFWbyrkx5faycpJIGez0E8HfDYk8QHTSv9KAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:49:38.890559Z"},"content_sha256":"2a9def1257f7c7590eb07b13b262ee28ec998d79dfa1b8aae66211c395093ad8","schema_version":"1.0","event_id":"sha256:2a9def1257f7c7590eb07b13b262ee28ec998d79dfa1b8aae66211c395093ad8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYHTUWS2C36OIEWZIPNKNTDINS/bundle.json","state_url":"https://pith.science/pith/OYHTUWS2C36OIEWZIPNKNTDINS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYHTUWS2C36OIEWZIPNKNTDINS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T10:49:38Z","links":{"resolver":"https://pith.science/pith/OYHTUWS2C36OIEWZIPNKNTDINS","bundle":"https://pith.science/pith/OYHTUWS2C36OIEWZIPNKNTDINS/bundle.json","state":"https://pith.science/pith/OYHTUWS2C36OIEWZIPNKNTDINS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYHTUWS2C36OIEWZIPNKNTDINS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OYHTUWS2C36OIEWZIPNKNTDINS","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":"77968b8168a906c49e3461eca0a1f1002f0d68c0d265b8a171d6bfa89c973218","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-17T12:53:25Z","title_canon_sha256":"5154b2697cceb62e965853f46195e7b31360c0a488e37e5fec2e896b73108ce3"},"schema_version":"1.0","source":{"id":"1411.4457","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4457","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4457v1","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4457","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"OYHTUWS2C36O","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OYHTUWS2C36OIEWZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OYHTUWS2","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:2a9def1257f7c7590eb07b13b262ee28ec998d79dfa1b8aae66211c395093ad8","target":"graph","created_at":"2026-05-18T00:44:28Z","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 a variety of results describing the possible diagonals of tuples of commuting hermitian operators in type $II_1$ factors. These results are generalisations of the classical Schur-Horn theorem to the infinite dimensional, multivariable setting. Our description of these possible diagonals uses a natural generalisation of the classical notion of majorization to the multivariable setting. In the special case when both the given tuple and the desired diagonal have finite joint spectrum, our results are complete. When the tuples do not have finite joint spectrum, we are able to prove strong","authors_text":"Mohan Ravichandran, Pedro Massey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-17T12:53:25Z","title":"Multivariable Schur-Horn theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4457","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:d9eddb08ddb3bb6d0265d13efc737dca7ac3997b53ada27d51d376249faf815a","target":"record","created_at":"2026-05-18T00:44:28Z","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":"77968b8168a906c49e3461eca0a1f1002f0d68c0d265b8a171d6bfa89c973218","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-17T12:53:25Z","title_canon_sha256":"5154b2697cceb62e965853f46195e7b31360c0a488e37e5fec2e896b73108ce3"},"schema_version":"1.0","source":{"id":"1411.4457","kind":"arxiv","version":1}},"canonical_sha256":"760f3a5a5a16fce412d943daa6cc686ca53f81535427238b7e0dda2ad2099995","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"760f3a5a5a16fce412d943daa6cc686ca53f81535427238b7e0dda2ad2099995","first_computed_at":"2026-05-18T00:44:28.676196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:28.676196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/xC0BlW0Q+PDK+rlbKDdDnCvS7ah9Pg+UqM4UuknDYaLgy/kQHnQAAurzbp5VEDqx2/a2blAtAH6ttl/1ReDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:28.676701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4457","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9eddb08ddb3bb6d0265d13efc737dca7ac3997b53ada27d51d376249faf815a","sha256:2a9def1257f7c7590eb07b13b262ee28ec998d79dfa1b8aae66211c395093ad8"],"state_sha256":"69b5ac6d2c7a64cd04e605222593f514dd08986f25c2788f839d8f69e8b40b8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4LCh6K4VjV5CYp58aIkoT85vITWlMPn719ZisNvNg30NddLgJaMcV4LmXZnb4TUTvSgaqgeCgzK/bUSolefRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:49:38.892465Z","bundle_sha256":"cebb1f4a21f7fe82c8b23a041ddc28b2fa09598eae976d83fbe250a6827eb176"}}