{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:P2HJO5IYN4PL27DO35AMENIJYC","short_pith_number":"pith:P2HJO5IY","schema_version":"1.0","canonical_sha256":"7e8e9775186f1ebd7c6edf40c23509c09394404b660cc97cfa98e7c197f88d6d","source":{"kind":"arxiv","id":"2302.07966","version":2},"attestation_state":"computed","paper":{"title":"The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AC","math.MP"],"primary_cat":"quant-ph","authors_text":"Rahul Sarkar, Theodore J. Yoder","submitted_at":"2023-02-15T22:06:40Z","abstract_excerpt":"Qudits with local dimension $d>2$ can have unique structure and uses that qubits ($d=2$) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group for any, including composite, $d$ in several ways. To cover composite values of $d$, we work with modules over commutative rings, which generalize the notion of vector spaces over fields. For any specified set of commutation relations, we construct a set of qudit Paulis satisfying those relations. We also study the maximum size of sets of Paulis that mutually"},"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":"2302.07966","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-02-15T22:06:40Z","cross_cats_sorted":["math-ph","math.AC","math.MP"],"title_canon_sha256":"b9bc8a1134957b959d47e34ef29f94a5450a3eb885346089a8b21aa4b5a9d8f4","abstract_canon_sha256":"aabdfc0d8818bf4a007fe16fcaeb996cc2422b6163a88f63d0dc852f568f555a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:05:47.909746Z","signature_b64":"RNqXNQegSinqcO7VLsFVTcRQLUm0GuQ09xJzEy/nVz6KY8DxJH754AkX7HSWlMJIcqbVA5u8gktarIDLQE4bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e8e9775186f1ebd7c6edf40c23509c09394404b660cc97cfa98e7c197f88d6d","last_reissued_at":"2026-07-05T08:05:47.909269Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:05:47.909269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AC","math.MP"],"primary_cat":"quant-ph","authors_text":"Rahul Sarkar, Theodore J. Yoder","submitted_at":"2023-02-15T22:06:40Z","abstract_excerpt":"Qudits with local dimension $d>2$ can have unique structure and uses that qubits ($d=2$) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group for any, including composite, $d$ in several ways. To cover composite values of $d$, we work with modules over commutative rings, which generalize the notion of vector spaces over fields. For any specified set of commutation relations, we construct a set of qudit Paulis satisfying those relations. We also study the maximum size of sets of Paulis that mutually"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.07966","kind":"arxiv","version":2},"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/2302.07966/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":"2302.07966","created_at":"2026-07-05T08:05:47.909325+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.07966v2","created_at":"2026-07-05T08:05:47.909325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.07966","created_at":"2026-07-05T08:05:47.909325+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2HJO5IYN4PL","created_at":"2026-07-05T08:05:47.909325+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2HJO5IYN4PL27DO","created_at":"2026-07-05T08:05:47.909325+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2HJO5IY","created_at":"2026-07-05T08:05:47.909325+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/P2HJO5IYN4PL27DO35AMENIJYC","json":"https://pith.science/pith/P2HJO5IYN4PL27DO35AMENIJYC.json","graph_json":"https://pith.science/api/pith-number/P2HJO5IYN4PL27DO35AMENIJYC/graph.json","events_json":"https://pith.science/api/pith-number/P2HJO5IYN4PL27DO35AMENIJYC/events.json","paper":"https://pith.science/paper/P2HJO5IY"},"agent_actions":{"view_html":"https://pith.science/pith/P2HJO5IYN4PL27DO35AMENIJYC","download_json":"https://pith.science/pith/P2HJO5IYN4PL27DO35AMENIJYC.json","view_paper":"https://pith.science/paper/P2HJO5IY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.07966&json=true","fetch_graph":"https://pith.science/api/pith-number/P2HJO5IYN4PL27DO35AMENIJYC/graph.json","fetch_events":"https://pith.science/api/pith-number/P2HJO5IYN4PL27DO35AMENIJYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2HJO5IYN4PL27DO35AMENIJYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2HJO5IYN4PL27DO35AMENIJYC/action/storage_attestation","attest_author":"https://pith.science/pith/P2HJO5IYN4PL27DO35AMENIJYC/action/author_attestation","sign_citation":"https://pith.science/pith/P2HJO5IYN4PL27DO35AMENIJYC/action/citation_signature","submit_replication":"https://pith.science/pith/P2HJO5IYN4PL27DO35AMENIJYC/action/replication_record"}},"created_at":"2026-07-05T08:05:47.909325+00:00","updated_at":"2026-07-05T08:05:47.909325+00:00"}