{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4QZS5NFFLECSPHGH65P6J7MZ27","short_pith_number":"pith:4QZS5NFF","schema_version":"1.0","canonical_sha256":"e4332eb4a55905279cc7f75fe4fd99d7de5b5881da78ad65868a1c985a0b2d8f","source":{"kind":"arxiv","id":"2512.00809","version":3},"attestation_state":"computed","paper":{"title":"Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Francesco Toppan, Zhanna Kuznetsova","submitted_at":"2025-11-30T09:37:15Z","abstract_excerpt":"We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups $Z_3^2$, $Z_2^p\\times Z_3^2$ for $p=1,2,3$, and investigate the properties of their associated multi-particle quantum paraoscillators. In the Rittenberg-Wyler's color Lie (super)algebras framework the above abelian groups are the simplest ones which induce mixed brackets interpolating commutators and anticommutators. These mixed brackets allow to accommodate two types of parastatistics: one based on the permutation group (beyond bosons and fermions in any space dimension) and an anyonic parastatistics based on the b"},"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":"2512.00809","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-11-30T09:37:15Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","quant-ph"],"title_canon_sha256":"57fc21a4f76affef27a200d7106c6fc61ede75352c37a435c25ccdf9245ac8a9","abstract_canon_sha256":"db374dacac74ff9dba61a46a49d8e0437e21050ec3587a46f6c50b4737e9f909"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:02:29.405595Z","signature_b64":"A7CkIyHQ0zTIqKMYYTzXmKxX7CzenPNA+2KCX5X9uwzd8tANlmwe/hnwmyfRDgan2e8vGhb+itJREpWD9ScNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4332eb4a55905279cc7f75fe4fd99d7de5b5881da78ad65868a1c985a0b2d8f","last_reissued_at":"2026-05-26T01:02:29.404524Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:02:29.404524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Francesco Toppan, Zhanna Kuznetsova","submitted_at":"2025-11-30T09:37:15Z","abstract_excerpt":"We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups $Z_3^2$, $Z_2^p\\times Z_3^2$ for $p=1,2,3$, and investigate the properties of their associated multi-particle quantum paraoscillators. In the Rittenberg-Wyler's color Lie (super)algebras framework the above abelian groups are the simplest ones which induce mixed brackets interpolating commutators and anticommutators. These mixed brackets allow to accommodate two types of parastatistics: one based on the permutation group (beyond bosons and fermions in any space dimension) and an anyonic parastatistics based on the b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.00809","kind":"arxiv","version":3},"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/2512.00809/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":"2512.00809","created_at":"2026-05-26T01:02:29.404693+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.00809v3","created_at":"2026-05-26T01:02:29.404693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.00809","created_at":"2026-05-26T01:02:29.404693+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QZS5NFFLECS","created_at":"2026-05-26T01:02:29.404693+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QZS5NFFLECSPHGH","created_at":"2026-05-26T01:02:29.404693+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QZS5NFF","created_at":"2026-05-26T01:02:29.404693+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.22178","citing_title":"Signature of paraparticles: a minimal Gedankenexperiment","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27","json":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27.json","graph_json":"https://pith.science/api/pith-number/4QZS5NFFLECSPHGH65P6J7MZ27/graph.json","events_json":"https://pith.science/api/pith-number/4QZS5NFFLECSPHGH65P6J7MZ27/events.json","paper":"https://pith.science/paper/4QZS5NFF"},"agent_actions":{"view_html":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27","download_json":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27.json","view_paper":"https://pith.science/paper/4QZS5NFF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.00809&json=true","fetch_graph":"https://pith.science/api/pith-number/4QZS5NFFLECSPHGH65P6J7MZ27/graph.json","fetch_events":"https://pith.science/api/pith-number/4QZS5NFFLECSPHGH65P6J7MZ27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27/action/storage_attestation","attest_author":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27/action/author_attestation","sign_citation":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27/action/citation_signature","submit_replication":"https://pith.science/pith/4QZS5NFFLECSPHGH65P6J7MZ27/action/replication_record"}},"created_at":"2026-05-26T01:02:29.404693+00:00","updated_at":"2026-05-26T01:02:29.404693+00:00"}