{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:QU4J4AMYBPBA4QWGYGWR4GL6K2","short_pith_number":"pith:QU4J4AMY","schema_version":"1.0","canonical_sha256":"85389e01980bc20e42c6c1ad1e197e5696323586cce956f297121b43ac64b320","source":{"kind":"arxiv","id":"2005.02009","version":1},"attestation_state":"computed","paper":{"title":"Informationally complete characters for quark and lepton mixings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT","quant-ph"],"primary_cat":"hep-ph","authors_text":"Klee Irwin, Marcelo M. Amaral, Michel Planat, Raymond Aschheim","submitted_at":"2020-05-05T08:48:52Z","abstract_excerpt":"A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters $\\kappa$ of a finite group $G$. Here we introduce a $d$-dimensional Hilbert space with $d=cc(G)$, the number of conjugacy classes of $G$. Groups under consideration should follow two rules, (a) the character table contains both two- and three-dimensional representations with at least one of them faithful and (b) there are minimal informationally complete measurements under the action of a $d$-dimensional Pauli group over the characters of these representations. Groups with small $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2005.02009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-05-05T08:48:52Z","cross_cats_sorted":["math.GR","math.RT","quant-ph"],"title_canon_sha256":"dda0920975235bf0b3a23485020316535c355d148993dd9c58b8ad43e8fd6612","abstract_canon_sha256":"aa44bd348d42895c9dee4e5e0e24b63d2dd08f4ecfe6cb3cf6bfe90f2ce5c4bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:11:13.722756Z","signature_b64":"evxEoDc7c1ReBUvE/quAuBeCGR1+1QmKcdNOomyfj/nf6h2JEANsk3nRdUdws6mmHD6qBh0H9n/q6Nyc4RBMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85389e01980bc20e42c6c1ad1e197e5696323586cce956f297121b43ac64b320","last_reissued_at":"2026-07-05T01:11:13.722344Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:11:13.722344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Informationally complete characters for quark and lepton mixings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT","quant-ph"],"primary_cat":"hep-ph","authors_text":"Klee Irwin, Marcelo M. Amaral, Michel Planat, Raymond Aschheim","submitted_at":"2020-05-05T08:48:52Z","abstract_excerpt":"A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters $\\kappa$ of a finite group $G$. Here we introduce a $d$-dimensional Hilbert space with $d=cc(G)$, the number of conjugacy classes of $G$. Groups under consideration should follow two rules, (a) the character table contains both two- and three-dimensional representations with at least one of them faithful and (b) there are minimal informationally complete measurements under the action of a $d$-dimensional Pauli group over the characters of these representations. Groups with small $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.02009","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.02009/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2005.02009","created_at":"2026-07-05T01:11:13.722398+00:00"},{"alias_kind":"arxiv_version","alias_value":"2005.02009v1","created_at":"2026-07-05T01:11:13.722398+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.02009","created_at":"2026-07-05T01:11:13.722398+00:00"},{"alias_kind":"pith_short_12","alias_value":"QU4J4AMYBPBA","created_at":"2026-07-05T01:11:13.722398+00:00"},{"alias_kind":"pith_short_16","alias_value":"QU4J4AMYBPBA4QWG","created_at":"2026-07-05T01:11:13.722398+00:00"},{"alias_kind":"pith_short_8","alias_value":"QU4J4AMY","created_at":"2026-07-05T01:11:13.722398+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2","json":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2.json","graph_json":"https://pith.science/api/pith-number/QU4J4AMYBPBA4QWGYGWR4GL6K2/graph.json","events_json":"https://pith.science/api/pith-number/QU4J4AMYBPBA4QWGYGWR4GL6K2/events.json","paper":"https://pith.science/paper/QU4J4AMY"},"agent_actions":{"view_html":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2","download_json":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2.json","view_paper":"https://pith.science/paper/QU4J4AMY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2005.02009&json=true","fetch_graph":"https://pith.science/api/pith-number/QU4J4AMYBPBA4QWGYGWR4GL6K2/graph.json","fetch_events":"https://pith.science/api/pith-number/QU4J4AMYBPBA4QWGYGWR4GL6K2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2/action/storage_attestation","attest_author":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2/action/author_attestation","sign_citation":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2/action/citation_signature","submit_replication":"https://pith.science/pith/QU4J4AMYBPBA4QWGYGWR4GL6K2/action/replication_record"}},"created_at":"2026-07-05T01:11:13.722398+00:00","updated_at":"2026-07-05T01:11:13.722398+00:00"}