{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DKMFPBQGCTVM3DCT3ZROUUENPI","short_pith_number":"pith:DKMFPBQG","canonical_record":{"source":{"id":"1201.1042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-01-05T00:37:54Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"0013118e2a62671ecc4ec4a875f34abeb3847fb490d5fef50f0d20461e1b7a21","abstract_canon_sha256":"9b26b35089f16fcce87ce4a98f82ff1dc1b35fdf11639e22c69315fe127e7ba7"},"schema_version":"1.0"},"canonical_sha256":"1a9857860614eacd8c53de62ea508d7a38215619600821e423c51b9c0b5abb44","source":{"kind":"arxiv","id":"1201.1042","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1042","created_at":"2026-05-18T01:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1042v2","created_at":"2026-05-18T01:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1042","created_at":"2026-05-18T01:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"DKMFPBQGCTVM","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DKMFPBQGCTVM3DCT","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DKMFPBQG","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DKMFPBQGCTVM3DCT3ZROUUENPI","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1042","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-01-05T00:37:54Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"0013118e2a62671ecc4ec4a875f34abeb3847fb490d5fef50f0d20461e1b7a21","abstract_canon_sha256":"9b26b35089f16fcce87ce4a98f82ff1dc1b35fdf11639e22c69315fe127e7ba7"},"schema_version":"1.0"},"canonical_sha256":"1a9857860614eacd8c53de62ea508d7a38215619600821e423c51b9c0b5abb44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:57.452121Z","signature_b64":"s2fAo01mCep62NitYpvWw0lTXK49n1YNuW9I3S0YCMbMiYszfkd9mBLvgDf/JAgpJTqyDgqBsDZZozj6lVxcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a9857860614eacd8c53de62ea508d7a38215619600821e423c51b9c0b5abb44","last_reissued_at":"2026-05-18T01:58:57.451543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:57.451543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1042","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":"2026-05-18T01:58:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hunKVuvq9LFWtzjMJGYxoCGVILvKozmimhfecOepSOTDhWL7W6y991PVKCY2pofZHqZbAiaoHFDGIyknSg6bDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:05:02.263437Z"},"content_sha256":"e892c419b2814242a9f4ea6153b9b1c2a446f9385bc9763e1a74ed6bcbd2c7c6","schema_version":"1.0","event_id":"sha256:e892c419b2814242a9f4ea6153b9b1c2a446f9385bc9763e1a74ed6bcbd2c7c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DKMFPBQGCTVM3DCT3ZROUUENPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mapping quantum-classical Liouville equation: projectors and trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.chem-ph","authors_text":"Aaron Kelly, Jeremy Schofield, Ramses van Zon, Raymond Kapral","submitted_at":"2012-01-05T00:37:54Z","abstract_excerpt":"The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1042","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":"2026-05-18T01:58:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ty/z0KdSaT68y+lBEEwossJ3mtm+r1NlUiDvlX9iISLNCY17nKdx3/fFP2ze7lo+5mzV5434yZ+ob/ydrBDrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:05:02.264069Z"},"content_sha256":"80148486a3f4f2a314e949686d66b2a0c051b0db658c329f18bcda1962b525dd","schema_version":"1.0","event_id":"sha256:80148486a3f4f2a314e949686d66b2a0c051b0db658c329f18bcda1962b525dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKMFPBQGCTVM3DCT3ZROUUENPI/bundle.json","state_url":"https://pith.science/pith/DKMFPBQGCTVM3DCT3ZROUUENPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKMFPBQGCTVM3DCT3ZROUUENPI/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":"2026-06-06T15:05:02Z","links":{"resolver":"https://pith.science/pith/DKMFPBQGCTVM3DCT3ZROUUENPI","bundle":"https://pith.science/pith/DKMFPBQGCTVM3DCT3ZROUUENPI/bundle.json","state":"https://pith.science/pith/DKMFPBQGCTVM3DCT3ZROUUENPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKMFPBQGCTVM3DCT3ZROUUENPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DKMFPBQGCTVM3DCT3ZROUUENPI","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":"9b26b35089f16fcce87ce4a98f82ff1dc1b35fdf11639e22c69315fe127e7ba7","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-01-05T00:37:54Z","title_canon_sha256":"0013118e2a62671ecc4ec4a875f34abeb3847fb490d5fef50f0d20461e1b7a21"},"schema_version":"1.0","source":{"id":"1201.1042","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1042","created_at":"2026-05-18T01:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1042v2","created_at":"2026-05-18T01:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1042","created_at":"2026-05-18T01:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"DKMFPBQGCTVM","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DKMFPBQGCTVM3DCT","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DKMFPBQG","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:80148486a3f4f2a314e949686d66b2a0c051b0db658c329f18bcda1962b525dd","target":"graph","created_at":"2026-05-18T01:58:57Z","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":"The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining projection operators onto the mapping states corresponding to the physical quantum states, it is shown that the mapping quantum-classical Liouville operator commutes with the projection operator so that the dynamics is confined to the physical space. It is also shown that a trajectory-based solution of this equation can be constructed that requires the simula","authors_text":"Aaron Kelly, Jeremy Schofield, Ramses van Zon, Raymond Kapral","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-01-05T00:37:54Z","title":"Mapping quantum-classical Liouville equation: projectors and trajectories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1042","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:e892c419b2814242a9f4ea6153b9b1c2a446f9385bc9763e1a74ed6bcbd2c7c6","target":"record","created_at":"2026-05-18T01:58:57Z","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":"9b26b35089f16fcce87ce4a98f82ff1dc1b35fdf11639e22c69315fe127e7ba7","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-01-05T00:37:54Z","title_canon_sha256":"0013118e2a62671ecc4ec4a875f34abeb3847fb490d5fef50f0d20461e1b7a21"},"schema_version":"1.0","source":{"id":"1201.1042","kind":"arxiv","version":2}},"canonical_sha256":"1a9857860614eacd8c53de62ea508d7a38215619600821e423c51b9c0b5abb44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a9857860614eacd8c53de62ea508d7a38215619600821e423c51b9c0b5abb44","first_computed_at":"2026-05-18T01:58:57.451543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:57.451543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s2fAo01mCep62NitYpvWw0lTXK49n1YNuW9I3S0YCMbMiYszfkd9mBLvgDf/JAgpJTqyDgqBsDZZozj6lVxcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:57.452121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1042","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e892c419b2814242a9f4ea6153b9b1c2a446f9385bc9763e1a74ed6bcbd2c7c6","sha256:80148486a3f4f2a314e949686d66b2a0c051b0db658c329f18bcda1962b525dd"],"state_sha256":"0593352771b805bed1f3061cb9f05a3dae8e96322aa1e3239419a4255e16cdf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BujKyP9DoJkWzQ1L2NLIuPwacP0kPB9H12w8W3KQpy+l2mNZiBWUMuYDC9gl1G7rkk+r2R9KenaBKTXoAJ1sCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:05:02.267365Z","bundle_sha256":"2ec6ceb51d23b889d828f833d1ac8c95b096885fc246055a446959dd7e462ef0"}}