{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FEWULJLYH7OSXEVK3WAIZWJLY7","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":"d235f55eec9ff02213822e03d29d5af6d9b2e7216b7ba5b368057c69690b7f6f","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-10T23:43:48Z","title_canon_sha256":"243b73410cff007eb2ddfe4fbd30cde072db234909c2373000a0b886423362ca"},"schema_version":"1.0","source":{"id":"1908.03828","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03828","created_at":"2026-07-04T23:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03828v2","created_at":"2026-07-04T23:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03828","created_at":"2026-07-04T23:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"FEWULJLYH7OS","created_at":"2026-07-04T23:59:08Z"},{"alias_kind":"pith_short_16","alias_value":"FEWULJLYH7OSXEVK","created_at":"2026-07-04T23:59:08Z"},{"alias_kind":"pith_short_8","alias_value":"FEWULJLY","created_at":"2026-07-04T23:59:08Z"}],"graph_snapshots":[{"event_id":"sha256:f8a750603345a47e70b080310937d76ea2397deb43de63e7ad6859f8eaf9f04c","target":"graph","created_at":"2026-07-04T23:59:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.03828/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The definition due to Accardi of a pair of complementary observables is adapted to the context of the Lie algebra $ su(2) $. We show that the pair of Pauli matrices $ A,B $ associated to the unit directions $ \\alpha $ and $ \\beta $ in $ \\mathbb{R}^{3} $ are Accardi complementary if and only if $ \\alpha $ and $ \\beta $ are orthogonal if and only if $ A $ and $ B $ are orthogonal. In particular, any pair of the standard triple of Pauli matrices is complementary.","authors_text":"Stephen Bruce Sontz","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-10T23:43:48Z","title":"Pauli Matrices: A Triple of Accardi Complementary Observables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03828","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:ade051d23f4df942d68b85e9b3b378fb78bc3ff192f0d5d3df4f43a54dc32ec2","target":"record","created_at":"2026-07-04T23:59:08Z","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":"d235f55eec9ff02213822e03d29d5af6d9b2e7216b7ba5b368057c69690b7f6f","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-10T23:43:48Z","title_canon_sha256":"243b73410cff007eb2ddfe4fbd30cde072db234909c2373000a0b886423362ca"},"schema_version":"1.0","source":{"id":"1908.03828","kind":"arxiv","version":2}},"canonical_sha256":"292d45a5783fdd2b92aadd808cd92bc7f235080ec7cc6e5995c1f035038b0c14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"292d45a5783fdd2b92aadd808cd92bc7f235080ec7cc6e5995c1f035038b0c14","first_computed_at":"2026-07-04T23:59:08.413364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:08.413364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G36fS/pxF73haYlySnu3zjMMGYb9+KbfyiNJO6OsYVMjxRgrhqtU9GR+wYzxdagZLV3ZB7dMUkTzJ2kNBEVpBg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:08.413799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03828","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ade051d23f4df942d68b85e9b3b378fb78bc3ff192f0d5d3df4f43a54dc32ec2","sha256:f8a750603345a47e70b080310937d76ea2397deb43de63e7ad6859f8eaf9f04c"],"state_sha256":"40a6ed3621724b800406b77d35d2a75c8cf4fc2921ec2b38ad48c051aed9f725"}