{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FZBGJVYSEZH4LK2VRBLAXV2AR3","short_pith_number":"pith:FZBGJVYS","schema_version":"1.0","canonical_sha256":"2e4264d712264fc5ab5588560bd7408ed34291327d9e55b4b1b3376ba0f6ce00","source":{"kind":"arxiv","id":"1212.2378","version":1},"attestation_state":"computed","paper":{"title":"1, 2, and 6 qubits, and the Ramanujan-Nagell theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. R. P. Rau, Yaroslav Pavlyukh","submitted_at":"2012-12-11T10:45:56Z","abstract_excerpt":"A conjecture of Ramanujan that was later proved by Nagell is used to show on the basis of matching dimensions that only three $n$-qubit systems, for $n=1, 2, 6$, can share an isomorphism of their symmetry groups with the rotation group of corresponding dimensions $3, 6, 91$. Topological analysis, however, rules out the last possibility."},"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":"1212.2378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-11T10:45:56Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"66b1454685602c6b2997307652cef4e4f98c9e8446f9a36725a468eedec7a3d2","abstract_canon_sha256":"1c5cd4e17badd2a0e3a68cb89f1a36d1e95a2fb0b4ec166bef115b684dbd5bb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:45.083748Z","signature_b64":"NM5wYTcNKq1v9FvblwLGHVSF+3OcfASxVEzRNpP56pFrxnxbe9M0caH8vD93vWU3yMgOa8QsRofhlRfBc1fGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e4264d712264fc5ab5588560bd7408ed34291327d9e55b4b1b3376ba0f6ce00","last_reissued_at":"2026-05-18T03:38:45.083084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:45.083084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"1, 2, and 6 qubits, and the Ramanujan-Nagell theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. R. P. Rau, Yaroslav Pavlyukh","submitted_at":"2012-12-11T10:45:56Z","abstract_excerpt":"A conjecture of Ramanujan that was later proved by Nagell is used to show on the basis of matching dimensions that only three $n$-qubit systems, for $n=1, 2, 6$, can share an isomorphism of their symmetry groups with the rotation group of corresponding dimensions $3, 6, 91$. Topological analysis, however, rules out the last possibility."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2378","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":""},"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":"1212.2378","created_at":"2026-05-18T03:38:45.083184+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.2378v1","created_at":"2026-05-18T03:38:45.083184+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2378","created_at":"2026-05-18T03:38:45.083184+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZBGJVYSEZH4","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZBGJVYSEZH4LK2V","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZBGJVYS","created_at":"2026-05-18T12:27:06.952714+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/FZBGJVYSEZH4LK2VRBLAXV2AR3","json":"https://pith.science/pith/FZBGJVYSEZH4LK2VRBLAXV2AR3.json","graph_json":"https://pith.science/api/pith-number/FZBGJVYSEZH4LK2VRBLAXV2AR3/graph.json","events_json":"https://pith.science/api/pith-number/FZBGJVYSEZH4LK2VRBLAXV2AR3/events.json","paper":"https://pith.science/paper/FZBGJVYS"},"agent_actions":{"view_html":"https://pith.science/pith/FZBGJVYSEZH4LK2VRBLAXV2AR3","download_json":"https://pith.science/pith/FZBGJVYSEZH4LK2VRBLAXV2AR3.json","view_paper":"https://pith.science/paper/FZBGJVYS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.2378&json=true","fetch_graph":"https://pith.science/api/pith-number/FZBGJVYSEZH4LK2VRBLAXV2AR3/graph.json","fetch_events":"https://pith.science/api/pith-number/FZBGJVYSEZH4LK2VRBLAXV2AR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZBGJVYSEZH4LK2VRBLAXV2AR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZBGJVYSEZH4LK2VRBLAXV2AR3/action/storage_attestation","attest_author":"https://pith.science/pith/FZBGJVYSEZH4LK2VRBLAXV2AR3/action/author_attestation","sign_citation":"https://pith.science/pith/FZBGJVYSEZH4LK2VRBLAXV2AR3/action/citation_signature","submit_replication":"https://pith.science/pith/FZBGJVYSEZH4LK2VRBLAXV2AR3/action/replication_record"}},"created_at":"2026-05-18T03:38:45.083184+00:00","updated_at":"2026-05-18T03:38:45.083184+00:00"}