{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:S7KM32WUHJN7H2OHHKAJOP45SA","short_pith_number":"pith:S7KM32WU","canonical_record":{"source":{"id":"1208.0720","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T11:38:24Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"bb3c36d6d57078cac446a1bf2be38e057e0837312e0820d39f3847eb8508a650","abstract_canon_sha256":"7744ddcb665f32f207bac8fe28b316455d00e7a8df2a2787f22c0361e3693667"},"schema_version":"1.0"},"canonical_sha256":"97d4cdead43a5bf3e9c73a80973f9d900f3b135420b623e01dbadf472955e971","source":{"kind":"arxiv","id":"1208.0720","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0720","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0720v2","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0720","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"pith_short_12","alias_value":"S7KM32WUHJN7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"S7KM32WUHJN7H2OH","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"S7KM32WU","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:S7KM32WUHJN7H2OHHKAJOP45SA","target":"record","payload":{"canonical_record":{"source":{"id":"1208.0720","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T11:38:24Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"bb3c36d6d57078cac446a1bf2be38e057e0837312e0820d39f3847eb8508a650","abstract_canon_sha256":"7744ddcb665f32f207bac8fe28b316455d00e7a8df2a2787f22c0361e3693667"},"schema_version":"1.0"},"canonical_sha256":"97d4cdead43a5bf3e9c73a80973f9d900f3b135420b623e01dbadf472955e971","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:23.407514Z","signature_b64":"RZ6K/zyAXT2O2IGBuqlOy2Hb/r+cH5yY5DL5ZzL7ENvplCxpcWRLaLW53jWS+yhgYagIc/7N+l+GF9Nbabp/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97d4cdead43a5bf3e9c73a80973f9d900f3b135420b623e01dbadf472955e971","last_reissued_at":"2026-05-18T01:55:23.406751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:23.406751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.0720","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":"2026-05-18T01:55:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LdH1cSY8OWrUwEunGBaVJhzyQF8th9fnRH2T9wv5Yqc+Nh2nf44rB7CEcJ5kofJ6BYK+pTio29Getr0ef9ogCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:19:38.050574Z"},"content_sha256":"0929fefd079be5801114880c0af6fecbe9cef1fd06493d89974bec486aa45c98","schema_version":"1.0","event_id":"sha256:0929fefd079be5801114880c0af6fecbe9cef1fd06493d89974bec486aa45c98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:S7KM32WUHJN7H2OHHKAJOP45SA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Maciej Blaszak, Ziemowit Domanski","submitted_at":"2012-08-03T11:38:24Z","abstract_excerpt":"This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum trajectory being an appropriate solution to quantum Hamiltonian equations is also a function defined on a classical phase space. The difference, when compare with classical theory, is in a deformation of a classical action of a flow on observables and states to an appropriate quantum action. This leads also to deformation of a multiplication rule for any quantum t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0720","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":"2026-05-18T01:55:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nwdfrBxGw6vbeiI9pAxqzcxzIXExAP5SsoMshV+JBdrCjJ18L3Q0I4glZWJqgAln6m1ty8300s/AzbN4bvCuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:19:38.051289Z"},"content_sha256":"d61a156b61f49050e17f89204c2d20d4cecef44e0f47e23da535b275039a2649","schema_version":"1.0","event_id":"sha256:d61a156b61f49050e17f89204c2d20d4cecef44e0f47e23da535b275039a2649"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7KM32WUHJN7H2OHHKAJOP45SA/bundle.json","state_url":"https://pith.science/pith/S7KM32WUHJN7H2OHHKAJOP45SA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7KM32WUHJN7H2OHHKAJOP45SA/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":"2026-06-06T23:19:38Z","links":{"resolver":"https://pith.science/pith/S7KM32WUHJN7H2OHHKAJOP45SA","bundle":"https://pith.science/pith/S7KM32WUHJN7H2OHHKAJOP45SA/bundle.json","state":"https://pith.science/pith/S7KM32WUHJN7H2OHHKAJOP45SA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7KM32WUHJN7H2OHHKAJOP45SA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:S7KM32WUHJN7H2OHHKAJOP45SA","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":"7744ddcb665f32f207bac8fe28b316455d00e7a8df2a2787f22c0361e3693667","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T11:38:24Z","title_canon_sha256":"bb3c36d6d57078cac446a1bf2be38e057e0837312e0820d39f3847eb8508a650"},"schema_version":"1.0","source":{"id":"1208.0720","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0720","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0720v2","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0720","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"pith_short_12","alias_value":"S7KM32WUHJN7","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"S7KM32WUHJN7H2OH","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"S7KM32WU","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:d61a156b61f49050e17f89204c2d20d4cecef44e0f47e23da535b275039a2649","target":"graph","created_at":"2026-05-18T01:55:23Z","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":"This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum trajectory being an appropriate solution to quantum Hamiltonian equations is also a function defined on a classical phase space. The difference, when compare with classical theory, is in a deformation of a classical action of a flow on observables and states to an appropriate quantum action. This leads also to deformation of a multiplication rule for any quantum t","authors_text":"Maciej Blaszak, Ziemowit Domanski","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T11:38:24Z","title":"Quantum trajectories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0720","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":"sha256:0929fefd079be5801114880c0af6fecbe9cef1fd06493d89974bec486aa45c98","target":"record","created_at":"2026-05-18T01:55:23Z","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":"7744ddcb665f32f207bac8fe28b316455d00e7a8df2a2787f22c0361e3693667","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-03T11:38:24Z","title_canon_sha256":"bb3c36d6d57078cac446a1bf2be38e057e0837312e0820d39f3847eb8508a650"},"schema_version":"1.0","source":{"id":"1208.0720","kind":"arxiv","version":2}},"canonical_sha256":"97d4cdead43a5bf3e9c73a80973f9d900f3b135420b623e01dbadf472955e971","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97d4cdead43a5bf3e9c73a80973f9d900f3b135420b623e01dbadf472955e971","first_computed_at":"2026-05-18T01:55:23.406751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:23.406751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RZ6K/zyAXT2O2IGBuqlOy2Hb/r+cH5yY5DL5ZzL7ENvplCxpcWRLaLW53jWS+yhgYagIc/7N+l+GF9Nbabp/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:23.407514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0720","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0929fefd079be5801114880c0af6fecbe9cef1fd06493d89974bec486aa45c98","sha256:d61a156b61f49050e17f89204c2d20d4cecef44e0f47e23da535b275039a2649"],"state_sha256":"0be3cbee4059425bd469b996efe716db926931718695b810f006defcb630219a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3dnTat6CtfHJFt7BOXR2pQ6h+mjowUoWoWZ2TkPEqv3kH06HENWoRxzTDJVm/HCGJHCojBuGiZEK2IjB5KTFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T23:19:38.055213Z","bundle_sha256":"84226af411405e2eba0497e1104f82139df5753db94b02b0e143ee337f20956a"}}