{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LGSLCD66MJVIE6UGNS3QEFBVZH","short_pith_number":"pith:LGSLCD66","canonical_record":{"source":{"id":"0910.3364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-18T11:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"e422ffce58e5aedb0d53e2b80df6904482315708b3b9df24f71db2372ffdf86d","abstract_canon_sha256":"62894f70d92623687f6c3cd6fadcfba767d9d9b196c7fce70959f4af475ff2a1"},"schema_version":"1.0"},"canonical_sha256":"59a4b10fde626a827a866cb7021435c9fbd21991ad1303c464452468864d77b4","source":{"kind":"arxiv","id":"0910.3364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3364","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3364v1","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3364","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"LGSLCD66MJVI","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LGSLCD66MJVIE6UG","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LGSLCD66","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LGSLCD66MJVIE6UGNS3QEFBVZH","target":"record","payload":{"canonical_record":{"source":{"id":"0910.3364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-18T11:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"e422ffce58e5aedb0d53e2b80df6904482315708b3b9df24f71db2372ffdf86d","abstract_canon_sha256":"62894f70d92623687f6c3cd6fadcfba767d9d9b196c7fce70959f4af475ff2a1"},"schema_version":"1.0"},"canonical_sha256":"59a4b10fde626a827a866cb7021435c9fbd21991ad1303c464452468864d77b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:14.609334Z","signature_b64":"bawgHw2vx7ZA5GJ9aW49lwEpzzgelC3rOuB1Zx4O4oMZvHUvhA56HhNuCMuwLEYp9v4hDUrid3c2iEQ7kn3zDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59a4b10fde626a827a866cb7021435c9fbd21991ad1303c464452468864d77b4","last_reissued_at":"2026-05-18T02:11:14.607933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:14.607933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.3364","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:11:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkKwfcD7B7e4gJr7v04oyxcQDxHqy9oCyDOpsWZBaDZdTNFJqp5uHQ/G0wxKubj/trHJPiMXdKljQRy2/WeaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:57:15.412678Z"},"content_sha256":"116cf8b4c8500ec935b52e42aa041e46c1cc7ab078d2e2e6626f0f117779f577","schema_version":"1.0","event_id":"sha256:116cf8b4c8500ec935b52e42aa041e46c1cc7ab078d2e2e6626f0f117779f577"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LGSLCD66MJVIE6UGNS3QEFBVZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Hong-chun Yuan, Hong-yi Fan","submitted_at":"2009-10-18T11:28:40Z","abstract_excerpt":"As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation about the Wigner operator (in its entangled form) in phase space quantum mechanics and its inverse transformation. In this way, some operator ordering problems can be solved and the contents of phase space quantum mechanics can be enriched."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3364","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:11:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VWPSHqK7OXb1CfaPsCFS3eVex6GX1qzQ2ioi1R/IizYqJd3tPObfEeGNyk2Syb83HbFq+pA07U/KFGV3Ic3+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:57:15.413019Z"},"content_sha256":"6f5b1fdc6be5e8742f524e98de7e8d6f793a77e15e35b3adcf65078e0ab8fca1","schema_version":"1.0","event_id":"sha256:6f5b1fdc6be5e8742f524e98de7e8d6f793a77e15e35b3adcf65078e0ab8fca1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGSLCD66MJVIE6UGNS3QEFBVZH/bundle.json","state_url":"https://pith.science/pith/LGSLCD66MJVIE6UGNS3QEFBVZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGSLCD66MJVIE6UGNS3QEFBVZH/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":"2026-06-21T09:57:15Z","links":{"resolver":"https://pith.science/pith/LGSLCD66MJVIE6UGNS3QEFBVZH","bundle":"https://pith.science/pith/LGSLCD66MJVIE6UGNS3QEFBVZH/bundle.json","state":"https://pith.science/pith/LGSLCD66MJVIE6UGNS3QEFBVZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGSLCD66MJVIE6UGNS3QEFBVZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LGSLCD66MJVIE6UGNS3QEFBVZH","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":"62894f70d92623687f6c3cd6fadcfba767d9d9b196c7fce70959f4af475ff2a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-18T11:28:40Z","title_canon_sha256":"e422ffce58e5aedb0d53e2b80df6904482315708b3b9df24f71db2372ffdf86d"},"schema_version":"1.0","source":{"id":"0910.3364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3364","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3364v1","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3364","created_at":"2026-05-18T02:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"LGSLCD66MJVI","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LGSLCD66MJVIE6UG","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LGSLCD66","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:6f5b1fdc6be5e8742f524e98de7e8d6f793a77e15e35b3adcf65078e0ab8fca1","target":"graph","created_at":"2026-05-18T02:11:14Z","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":"As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation about the Wigner operator (in its entangled form) in phase space quantum mechanics and its inverse transformation. In this way, some operator ordering problems can be solved and the contents of phase space quantum mechanics can be enriched.","authors_text":"Hong-chun Yuan, Hong-yi Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-18T11:28:40Z","title":"New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3364","kind":"arxiv","version":1},"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":"sha256:116cf8b4c8500ec935b52e42aa041e46c1cc7ab078d2e2e6626f0f117779f577","target":"record","created_at":"2026-05-18T02:11:14Z","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":"62894f70d92623687f6c3cd6fadcfba767d9d9b196c7fce70959f4af475ff2a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-18T11:28:40Z","title_canon_sha256":"e422ffce58e5aedb0d53e2b80df6904482315708b3b9df24f71db2372ffdf86d"},"schema_version":"1.0","source":{"id":"0910.3364","kind":"arxiv","version":1}},"canonical_sha256":"59a4b10fde626a827a866cb7021435c9fbd21991ad1303c464452468864d77b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59a4b10fde626a827a866cb7021435c9fbd21991ad1303c464452468864d77b4","first_computed_at":"2026-05-18T02:11:14.607933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:14.607933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bawgHw2vx7ZA5GJ9aW49lwEpzzgelC3rOuB1Zx4O4oMZvHUvhA56HhNuCMuwLEYp9v4hDUrid3c2iEQ7kn3zDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:14.609334Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.3364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:116cf8b4c8500ec935b52e42aa041e46c1cc7ab078d2e2e6626f0f117779f577","sha256:6f5b1fdc6be5e8742f524e98de7e8d6f793a77e15e35b3adcf65078e0ab8fca1"],"state_sha256":"1f736602655ec0975d8b88885b0008440b97d0177abe05b8c78d4cede6bba6f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wl/JpCFRRcPk/nGDMVG4SR0YHosDru2xXRbgthHWNhk72KoHZYpdvJvqSF08Py9084jirJKoLjNxLTRWuT0sAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:57:15.414872Z","bundle_sha256":"337c62f505c69d5b3851d49192844c3f18e7c6cab19371483f914ed146ec1431"}}