{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KLDJ2JAGDK2NEMJCJCZFTE36MG","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":"8e59fc84dd5745be6ad0da7049c48729655ed91b85ff397e92894f52dc77fe12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2022-08-25T11:18:25Z","title_canon_sha256":"a586f0eda361f1f6b5ca7972f0b77cc4d538bb2b6d3809f72079f4a9e480c84d"},"schema_version":"1.0","source":{"id":"2208.12006","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.12006","created_at":"2026-07-05T07:50:18Z"},{"alias_kind":"arxiv_version","alias_value":"2208.12006v3","created_at":"2026-07-05T07:50:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.12006","created_at":"2026-07-05T07:50:18Z"},{"alias_kind":"pith_short_12","alias_value":"KLDJ2JAGDK2N","created_at":"2026-07-05T07:50:18Z"},{"alias_kind":"pith_short_16","alias_value":"KLDJ2JAGDK2NEMJC","created_at":"2026-07-05T07:50:18Z"},{"alias_kind":"pith_short_8","alias_value":"KLDJ2JAG","created_at":"2026-07-05T07:50:18Z"}],"graph_snapshots":[{"event_id":"sha256:7051c663d61f3f1f7bea1e6f5d4a59c991ce49be1d3d9aa1a3c14bd45324cd14","target":"graph","created_at":"2026-07-05T07:50:18Z","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/2208.12006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schr\\\"{o}dinger equation. Because a perturbation is represented by unitary transformation in quantum dynamics, we calculate phase response curves with respect to generators of a Lie algebra. Our method shows that the continuous measurement yields phase clusters and alters the phase response curves. The observable clusters capture the phase dynamics of individual quantum oscillators,","authors_text":"Wataru Setoyama, Yoshihiko Hasegawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2022-08-25T11:18:25Z","title":"Lie Algebraic Quantum Phase Reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.12006","kind":"arxiv","version":3},"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":"sha256:9a4fd2e60ad30c3f6fb9f33a9bcda217cff232cecbf464ad111cfe6a202ff5f6","target":"record","created_at":"2026-07-05T07:50:18Z","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":"8e59fc84dd5745be6ad0da7049c48729655ed91b85ff397e92894f52dc77fe12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2022-08-25T11:18:25Z","title_canon_sha256":"a586f0eda361f1f6b5ca7972f0b77cc4d538bb2b6d3809f72079f4a9e480c84d"},"schema_version":"1.0","source":{"id":"2208.12006","kind":"arxiv","version":3}},"canonical_sha256":"52c69d24061ab4d2312248b259937e61af10bfa42ee7858e3ec8f05c3fb55377","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52c69d24061ab4d2312248b259937e61af10bfa42ee7858e3ec8f05c3fb55377","first_computed_at":"2026-07-05T07:50:18.412778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:50:18.412778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gmxL/WLLaRTcWK/qr5C5dJ/edTP50Bzs8nuq4DSaumLXJgp0z8fwuGriY0sRDErJ1iOThSXjzCVeH0RFAQuhAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:50:18.413206Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.12006","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a4fd2e60ad30c3f6fb9f33a9bcda217cff232cecbf464ad111cfe6a202ff5f6","sha256:7051c663d61f3f1f7bea1e6f5d4a59c991ce49be1d3d9aa1a3c14bd45324cd14"],"state_sha256":"3f4ac0c372990f985bad193c51e27025d4f6f3b50314faed6f69c1cc31fcffba"}