{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MMX26XOVCYBO3GIEOVRL3NRGR5","short_pith_number":"pith:MMX26XOV","canonical_record":{"source":{"id":"1412.1158","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-03T01:59:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"97506b9f55557e84976a9a76b3fb46c7fdb7677a28677bbab080fc2e981d3849","abstract_canon_sha256":"0d6250ca4a63d3aeac53c8eabb0b754c4a5fe34491e607e92b7e11092746c9a9"},"schema_version":"1.0"},"canonical_sha256":"632faf5dd51602ed99047562bdb6268f4d777739ce7ba251488ef108b2ed2804","source":{"kind":"arxiv","id":"1412.1158","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1158","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1158v2","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1158","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"MMX26XOVCYBO","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MMX26XOVCYBO3GIE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MMX26XOV","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MMX26XOVCYBO3GIEOVRL3NRGR5","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1158","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-03T01:59:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"97506b9f55557e84976a9a76b3fb46c7fdb7677a28677bbab080fc2e981d3849","abstract_canon_sha256":"0d6250ca4a63d3aeac53c8eabb0b754c4a5fe34491e607e92b7e11092746c9a9"},"schema_version":"1.0"},"canonical_sha256":"632faf5dd51602ed99047562bdb6268f4d777739ce7ba251488ef108b2ed2804","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:31.219069Z","signature_b64":"pSRJ5CCwHEOr1n2ZWOrG5Gs9H+oEEkJ1A3AQHsfu0+R4Qa1UPOcI5aZpNoea+To35CAQL5p5IP5XFlTIR1laCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"632faf5dd51602ed99047562bdb6268f4d777739ce7ba251488ef108b2ed2804","last_reissued_at":"2026-05-18T02:28:31.218454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:31.218454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1158","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"up/OX/nDFA1jjh6IWL6mUatXiakQxP+z1Tq+brL6UKxXZh1g1M6NJ9GfI2wdSTubmjOso5Gc9ex+0azk2TrwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:49:32.128613Z"},"content_sha256":"c2ba55da3d4b13b4beb37bfaff84813d075497099cff5aaf29c7034d540e2490","schema_version":"1.0","event_id":"sha256:c2ba55da3d4b13b4beb37bfaff84813d075497099cff5aaf29c7034d540e2490"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MMX26XOVCYBO3GIEOVRL3NRGR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Qubits, Weyl spinors, quantum NOT gates, and dynamical decoupling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"R. Romero","submitted_at":"2014-12-03T01:59:04Z","abstract_excerpt":"An equivalence is established between orthogonal pure state qubits on the Bloch sphere and massless Weyl spinors, when the Bloch vector is taken as the physical three-momentum. A family of unitary, coordinate dependent transformations is obtained which connects orthogonal combinations of the basis states of a two-level quantum system. It is shown that a subset of these transformations possesses the novel feature of effecting a point inversion by means of a rotation. For qubits, these transformations act as quantum NOT/parity gates, and also as flipping operators that exactly cancel decoherence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1158","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MsNM1bfUT3Lbr5m2m3QYyMJTYARJmmLdamDRFkxwp7EmKLdiiqFd964NwPkkV0Jz5e8bTCdxLfRc7ma/57xdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:49:32.129230Z"},"content_sha256":"1d4d7a2742db1df3845b6d4931f6fc0b0ddbde4d822cb1f5526bb69f79e4672e","schema_version":"1.0","event_id":"sha256:1d4d7a2742db1df3845b6d4931f6fc0b0ddbde4d822cb1f5526bb69f79e4672e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MMX26XOVCYBO3GIEOVRL3NRGR5/bundle.json","state_url":"https://pith.science/pith/MMX26XOVCYBO3GIEOVRL3NRGR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MMX26XOVCYBO3GIEOVRL3NRGR5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T21:49:32Z","links":{"resolver":"https://pith.science/pith/MMX26XOVCYBO3GIEOVRL3NRGR5","bundle":"https://pith.science/pith/MMX26XOVCYBO3GIEOVRL3NRGR5/bundle.json","state":"https://pith.science/pith/MMX26XOVCYBO3GIEOVRL3NRGR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MMX26XOVCYBO3GIEOVRL3NRGR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MMX26XOVCYBO3GIEOVRL3NRGR5","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":"0d6250ca4a63d3aeac53c8eabb0b754c4a5fe34491e607e92b7e11092746c9a9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-03T01:59:04Z","title_canon_sha256":"97506b9f55557e84976a9a76b3fb46c7fdb7677a28677bbab080fc2e981d3849"},"schema_version":"1.0","source":{"id":"1412.1158","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1158","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1158v2","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1158","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"MMX26XOVCYBO","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MMX26XOVCYBO3GIE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MMX26XOV","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:1d4d7a2742db1df3845b6d4931f6fc0b0ddbde4d822cb1f5526bb69f79e4672e","target":"graph","created_at":"2026-05-18T02:28:31Z","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"},"paper":{"abstract_excerpt":"An equivalence is established between orthogonal pure state qubits on the Bloch sphere and massless Weyl spinors, when the Bloch vector is taken as the physical three-momentum. A family of unitary, coordinate dependent transformations is obtained which connects orthogonal combinations of the basis states of a two-level quantum system. It is shown that a subset of these transformations possesses the novel feature of effecting a point inversion by means of a rotation. For qubits, these transformations act as quantum NOT/parity gates, and also as flipping operators that exactly cancel decoherence","authors_text":"R. Romero","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-03T01:59:04Z","title":"Qubits, Weyl spinors, quantum NOT gates, and dynamical decoupling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1158","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:c2ba55da3d4b13b4beb37bfaff84813d075497099cff5aaf29c7034d540e2490","target":"record","created_at":"2026-05-18T02:28:31Z","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":"0d6250ca4a63d3aeac53c8eabb0b754c4a5fe34491e607e92b7e11092746c9a9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-12-03T01:59:04Z","title_canon_sha256":"97506b9f55557e84976a9a76b3fb46c7fdb7677a28677bbab080fc2e981d3849"},"schema_version":"1.0","source":{"id":"1412.1158","kind":"arxiv","version":2}},"canonical_sha256":"632faf5dd51602ed99047562bdb6268f4d777739ce7ba251488ef108b2ed2804","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"632faf5dd51602ed99047562bdb6268f4d777739ce7ba251488ef108b2ed2804","first_computed_at":"2026-05-18T02:28:31.218454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:31.218454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pSRJ5CCwHEOr1n2ZWOrG5Gs9H+oEEkJ1A3AQHsfu0+R4Qa1UPOcI5aZpNoea+To35CAQL5p5IP5XFlTIR1laCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:31.219069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1158","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2ba55da3d4b13b4beb37bfaff84813d075497099cff5aaf29c7034d540e2490","sha256:1d4d7a2742db1df3845b6d4931f6fc0b0ddbde4d822cb1f5526bb69f79e4672e"],"state_sha256":"bbb52b608f46c53447df8b18bbe7b9f41743676d93b3cce8a2943931cd6d81d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DGE4ujfitkYnT4gUUCafA4a+oXM3ZZHRmh94Q0GbVHVLzWQ8uGhRMRELcxUzuam/KGLE9/7XmhfVHBpotBmAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:49:32.132923Z","bundle_sha256":"3d6597796736cbba4a6cfaf98e45194744ac96964d228e9611ad1ac80ca2bd9a"}}