{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TS3WCVIUOFPKWFQX5IGKP5ONEM","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":"7c8814e0d91e1c549b93ef055b873716f0f386da7f87a6b01bd23fa11ee284df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-07-24T01:43:56Z","title_canon_sha256":"c4eda6b254062ea8bb940dfbcb20fe85c5105d1b20402f512d6b836a37403fc2"},"schema_version":"1.0","source":{"id":"2107.11507","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.11507","created_at":"2026-07-05T04:24:55Z"},{"alias_kind":"arxiv_version","alias_value":"2107.11507v2","created_at":"2026-07-05T04:24:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.11507","created_at":"2026-07-05T04:24:55Z"},{"alias_kind":"pith_short_12","alias_value":"TS3WCVIUOFPK","created_at":"2026-07-05T04:24:55Z"},{"alias_kind":"pith_short_16","alias_value":"TS3WCVIUOFPKWFQX","created_at":"2026-07-05T04:24:55Z"},{"alias_kind":"pith_short_8","alias_value":"TS3WCVIU","created_at":"2026-07-05T04:24:55Z"}],"graph_snapshots":[{"event_id":"sha256:220edb0ec407d7155d6daadfd27326a04bca9beca2c066d218984c9efef9aa8e","target":"graph","created_at":"2026-07-05T04:24:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.11507/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a tuple $(Y_1,\\dots,Y_d)$ of normal operators in a tracial operator algebra setting with prescribed sizes of the eigenspaces for each $Y_i$. We address the question what one can say about the sizes of the eigenspaces for any non-commutative polynomial $P(Y_1,\\dots,Y_d)$ in those operators? We show that for each polynomial $P$ there are unavoidable eigenspaces, which occur in $P(Y_1,\\dots,Y_d)$ for any $(Y_1,\\dots,Y_d)$ with the prescribed eigenspaces for the marginals. We will describe this minimal situation both in algebraic terms - where it is given by realizations via matrices over","authors_text":"Guillaume C\\'ebron, Octavio Arizmendi, Roland Speicher, Sheng Yin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-07-24T01:43:56Z","title":"Universality of free random variables: atoms for non-commutative rational functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.11507","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":"sha256:3ad5783082fe8b61156b6b5ba8f520e9e3bef8d5c4dc329d42357753864708f2","target":"record","created_at":"2026-07-05T04:24:55Z","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":"7c8814e0d91e1c549b93ef055b873716f0f386da7f87a6b01bd23fa11ee284df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-07-24T01:43:56Z","title_canon_sha256":"c4eda6b254062ea8bb940dfbcb20fe85c5105d1b20402f512d6b836a37403fc2"},"schema_version":"1.0","source":{"id":"2107.11507","kind":"arxiv","version":2}},"canonical_sha256":"9cb7615514715eab1617ea0ca7f5cd23038afa1b9e8d43c049bf9b986df5b5a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cb7615514715eab1617ea0ca7f5cd23038afa1b9e8d43c049bf9b986df5b5a4","first_computed_at":"2026-07-05T04:24:55.960358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:24:55.960358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XANIEeV81t4JbgZsQemDswp94O5Cyj/YsZ2nSbahAdiUoQT5SayQ1qnhX/ynWdyz6IXyMd/ynJx3D/toe5uwCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:24:55.960835Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.11507","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ad5783082fe8b61156b6b5ba8f520e9e3bef8d5c4dc329d42357753864708f2","sha256:220edb0ec407d7155d6daadfd27326a04bca9beca2c066d218984c9efef9aa8e"],"state_sha256":"7fba9e1b664cb3a585432f378bf53695b092728251956531c124140d82d9647f"}