{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JAGR4S2DIIP755HMCOKBVDLJCM","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":"22617f530e1819ba22251a49642a58d306158e89bf530a04299676ec444bdc84","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-03-15T09:32:43Z","title_canon_sha256":"7e6c899e3cfedcb34967d94ec1d7e7109fd36b8d6cc56cad8d32fd88b37b40d2"},"schema_version":"1.0","source":{"id":"1803.05658","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05658","created_at":"2026-05-18T00:16:42Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05658v2","created_at":"2026-05-18T00:16:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05658","created_at":"2026-05-18T00:16:42Z"},{"alias_kind":"pith_short_12","alias_value":"JAGR4S2DIIP7","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JAGR4S2DIIP755HM","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JAGR4S2D","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:6db9c934100edd2538a3d435876c6017b2a474ab99442ba860528cb334d89e9e","target":"graph","created_at":"2026-05-18T00:16:42Z","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 ask the question whether for a given unitary representation $U$ the associated operator $\\rho_{U}\\in\\operatorname{Mor}(U,U^{c\\, c})$ has spectrum invariant under inversion -- in this case we say that $\\rho_{U}$ has symmetric eigenvalues. This does not have to be the case. However, we give affirmative answer whenever a certain condition on the growth of dimensions of irreducible subrepresentations of tensor powers of $U$ is imposed. This condition is satisfied whenever $\\widehat{\\mathbb{G}}$ is of subexponential growth.","authors_text":"Jacek Krajczok","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-03-15T09:32:43Z","title":"Symmetry of eigenvalues of operators associated with representations of compact quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05658","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:b39a2563e8aa0bb119024421ba1a451d200a54c0c0402b2fea32abd2b4dc62ac","target":"record","created_at":"2026-05-18T00:16:42Z","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":"22617f530e1819ba22251a49642a58d306158e89bf530a04299676ec444bdc84","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-03-15T09:32:43Z","title_canon_sha256":"7e6c899e3cfedcb34967d94ec1d7e7109fd36b8d6cc56cad8d32fd88b37b40d2"},"schema_version":"1.0","source":{"id":"1803.05658","kind":"arxiv","version":2}},"canonical_sha256":"480d1e4b43421ffef4ec13941a8d691330d6bce5ee6ec37018ba959b8ecf5fb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"480d1e4b43421ffef4ec13941a8d691330d6bce5ee6ec37018ba959b8ecf5fb8","first_computed_at":"2026-05-18T00:16:42.057171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:42.057171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y4EK1r4lsK1s4hbx01urU5UaajoNHl7wTL06UX5k3C81HD1MWN+R7lF618SX4urH/m1mWrid7vgmwd7/Kok0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:42.057920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05658","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b39a2563e8aa0bb119024421ba1a451d200a54c0c0402b2fea32abd2b4dc62ac","sha256:6db9c934100edd2538a3d435876c6017b2a474ab99442ba860528cb334d89e9e"],"state_sha256":"71fb68c0103dd5c39af3ddbfd13ed2798f38d735fe40b60a226fcc12b6b61112"}