{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WWMV66TD74B3AQG7PFGMBRXCB7","short_pith_number":"pith:WWMV66TD","canonical_record":{"source":{"id":"1312.2005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-06T21:05:30Z","cross_cats_sorted":["physics.chem-ph"],"title_canon_sha256":"04aa69c118e37139802611472b1f91cb4da14d71c58cc0f3bf2392b1e541aee9","abstract_canon_sha256":"3a860d9c62b300ba8e98231dfccff173ab43ce831fbe577850a88880f9ae7f46"},"schema_version":"1.0"},"canonical_sha256":"b5995f7a63ff03b040df794cc0c6e20fdbfc751314ce4ba86d24f3e665406b05","source":{"kind":"arxiv","id":"1312.2005","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2005","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2005v1","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2005","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"WWMV66TD74B3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WWMV66TD74B3AQG7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WWMV66TD","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WWMV66TD74B3AQG7PFGMBRXCB7","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-06T21:05:30Z","cross_cats_sorted":["physics.chem-ph"],"title_canon_sha256":"04aa69c118e37139802611472b1f91cb4da14d71c58cc0f3bf2392b1e541aee9","abstract_canon_sha256":"3a860d9c62b300ba8e98231dfccff173ab43ce831fbe577850a88880f9ae7f46"},"schema_version":"1.0"},"canonical_sha256":"b5995f7a63ff03b040df794cc0c6e20fdbfc751314ce4ba86d24f3e665406b05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:45.618174Z","signature_b64":"qoFJtYVmxv24WrUoizZ4yp+JJ3HlaSA+z6dQUCH/qshnre+HNc3hXQwYJL2TzfLgdXlTJi0QG2B+COCaI4ADCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5995f7a63ff03b040df794cc0c6e20fdbfc751314ce4ba86d24f3e665406b05","last_reissued_at":"2026-05-18T02:29:45.617762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:45.617762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2005","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":"2026-05-18T02:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OuXRR0wjlkPNFzo9px4aZ4RPJcbdtaVvNeM0S5rHxQG4Aa1+/UzLOpve8bydNLzvn1kFryD8cxXg42AxjPouBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T22:49:58.536726Z"},"content_sha256":"87a1cbfe5b4c382b6903ade39e7d15db08a6a3545e7677800841c4daa0d2f0c3","schema_version":"1.0","event_id":"sha256:87a1cbfe5b4c382b6903ade39e7d15db08a6a3545e7677800841c4daa0d2f0c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WWMV66TD74B3AQG7PFGMBRXCB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of geometric phase effects in the quantum-classical Liouville formalism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Artur F. Izmaylov, Chang-Yu Hsieh, Ilya G. Ryabinkin, Raymond Kapral","submitted_at":"2013-12-06T21:05:30Z","abstract_excerpt":"We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of doub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2005","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":"2026-05-18T02:29:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1qmAdM/cAN+VCcTUYalPA/UDAhzK+9PF6taQ7Srw2qR+xii+5WJc9rgZM/W1+kO0YtdaiCmM3+MEeb4HFicBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T22:49:58.537068Z"},"content_sha256":"94f0a84e4230d827437139672eed245df430e43d933bcad6bb09f64cb6d5265f","schema_version":"1.0","event_id":"sha256:94f0a84e4230d827437139672eed245df430e43d933bcad6bb09f64cb6d5265f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWMV66TD74B3AQG7PFGMBRXCB7/bundle.json","state_url":"https://pith.science/pith/WWMV66TD74B3AQG7PFGMBRXCB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWMV66TD74B3AQG7PFGMBRXCB7/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":"2026-05-19T22:49:58Z","links":{"resolver":"https://pith.science/pith/WWMV66TD74B3AQG7PFGMBRXCB7","bundle":"https://pith.science/pith/WWMV66TD74B3AQG7PFGMBRXCB7/bundle.json","state":"https://pith.science/pith/WWMV66TD74B3AQG7PFGMBRXCB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWMV66TD74B3AQG7PFGMBRXCB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WWMV66TD74B3AQG7PFGMBRXCB7","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":"3a860d9c62b300ba8e98231dfccff173ab43ce831fbe577850a88880f9ae7f46","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-06T21:05:30Z","title_canon_sha256":"04aa69c118e37139802611472b1f91cb4da14d71c58cc0f3bf2392b1e541aee9"},"schema_version":"1.0","source":{"id":"1312.2005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2005","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2005v1","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2005","created_at":"2026-05-18T02:29:45Z"},{"alias_kind":"pith_short_12","alias_value":"WWMV66TD74B3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WWMV66TD74B3AQG7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WWMV66TD","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:94f0a84e4230d827437139672eed245df430e43d933bcad6bb09f64cb6d5265f","target":"graph","created_at":"2026-05-18T02:29:45Z","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":"We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of doub","authors_text":"Artur F. Izmaylov, Chang-Yu Hsieh, Ilya G. Ryabinkin, Raymond Kapral","cross_cats":["physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-06T21:05:30Z","title":"Analysis of geometric phase effects in the quantum-classical Liouville formalism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2005","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":"sha256:87a1cbfe5b4c382b6903ade39e7d15db08a6a3545e7677800841c4daa0d2f0c3","target":"record","created_at":"2026-05-18T02:29:45Z","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":"3a860d9c62b300ba8e98231dfccff173ab43ce831fbe577850a88880f9ae7f46","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-06T21:05:30Z","title_canon_sha256":"04aa69c118e37139802611472b1f91cb4da14d71c58cc0f3bf2392b1e541aee9"},"schema_version":"1.0","source":{"id":"1312.2005","kind":"arxiv","version":1}},"canonical_sha256":"b5995f7a63ff03b040df794cc0c6e20fdbfc751314ce4ba86d24f3e665406b05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5995f7a63ff03b040df794cc0c6e20fdbfc751314ce4ba86d24f3e665406b05","first_computed_at":"2026-05-18T02:29:45.617762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:45.617762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qoFJtYVmxv24WrUoizZ4yp+JJ3HlaSA+z6dQUCH/qshnre+HNc3hXQwYJL2TzfLgdXlTJi0QG2B+COCaI4ADCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:45.618174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87a1cbfe5b4c382b6903ade39e7d15db08a6a3545e7677800841c4daa0d2f0c3","sha256:94f0a84e4230d827437139672eed245df430e43d933bcad6bb09f64cb6d5265f"],"state_sha256":"63890530b9d67187a9e32610f79ecde93303559a965f044e227faa9d4b30bf77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AaVPaRKI7X9A77E0mF8E4Y58yqKFcGBM91ZjqqCSo3dAMz494HjlJI5QemsAPwVvU1Tm3GaJ6fm3EgysUHQ1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T22:49:58.539147Z","bundle_sha256":"47911aa404a4ea67d131ec17ed56414a0aa6baef63e0c1e5c9c839c99667f990"}}