{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:XGPHHQVU76IZ5GI25BM6SHFRMK","short_pith_number":"pith:XGPHHQVU","canonical_record":{"source":{"id":"0902.0646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-03T23:55:20Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"744e128f012e858409b15263e070aca2d79ae24a4d37cbd42b11d5c8a6cbb6be","abstract_canon_sha256":"839bcdd902bb727c58bb5c215885357e77c44844a48d13bc70dc8bb640d935e0"},"schema_version":"1.0"},"canonical_sha256":"b99e73c2b4ff919e991ae859e91cb1629d6c0bee91b27b415e197a91e9690487","source":{"kind":"arxiv","id":"0902.0646","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0646","created_at":"2026-05-18T02:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0646v1","created_at":"2026-05-18T02:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0646","created_at":"2026-05-18T02:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"XGPHHQVU76IZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XGPHHQVU76IZ5GI2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XGPHHQVU","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:XGPHHQVU76IZ5GI25BM6SHFRMK","target":"record","payload":{"canonical_record":{"source":{"id":"0902.0646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-03T23:55:20Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"744e128f012e858409b15263e070aca2d79ae24a4d37cbd42b11d5c8a6cbb6be","abstract_canon_sha256":"839bcdd902bb727c58bb5c215885357e77c44844a48d13bc70dc8bb640d935e0"},"schema_version":"1.0"},"canonical_sha256":"b99e73c2b4ff919e991ae859e91cb1629d6c0bee91b27b415e197a91e9690487","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:54.341945Z","signature_b64":"zky1t4wiBWlkxuz6nImVW/uzcxpMOBj0tBQlaiJwIFPEALYgD+9LUylenShv8t4Z4U1x1PJr/zIhULFlCJeNAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b99e73c2b4ff919e991ae859e91cb1629d6c0bee91b27b415e197a91e9690487","last_reissued_at":"2026-05-18T02:14:54.341345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:54.341345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.0646","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":"2026-05-18T02:14:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kYoIJfAvialXmpjgeZBgkMSRoLHCKLD3VUDd1+F870P1DOyosNLEUpofKyEFS384mxAhfWhRDnBNOblKKiwtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:58:33.417685Z"},"content_sha256":"3e6280ff10bae6aeb596606bdd8e35e11f5edc8cf22f75a701f0c209aff45387","schema_version":"1.0","event_id":"sha256:3e6280ff10bae6aeb596606bdd8e35e11f5edc8cf22f75a701f0c209aff45387"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:XGPHHQVU76IZ5GI25BM6SHFRMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Superadiabatic transition histories in quantum molecular dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Benjamin D. Goddard, Stefan Teufel, Volker Betz","submitted_at":"2009-02-03T23:55:20Z","abstract_excerpt":"We study the dynamics of a molecule's nuclear wave-function near an avoided crossing of two electronic energy levels, for one nuclear degree of freedom. We derive the general form of the Schroedinger equation in the n-th superadiabatic representation for all n, and give some partial results about the asymptotics for large n. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace, when a wave packet crosses the transition region. In the optimal superadiabatic representation, which we define, this c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0646","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":"2026-05-18T02:14:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVBsWhNi0CnUgijWFk79dp7fPNLgj3dSGwt1ybk1Pz0fCw6K6+NAPX2hY+Oe7PmWXUC1TBWIl18EnwVmu4NKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:58:33.418043Z"},"content_sha256":"05039193a37143af0fd11d0be5aea1aa740bc1c412f4ba7ba914e20cb913656c","schema_version":"1.0","event_id":"sha256:05039193a37143af0fd11d0be5aea1aa740bc1c412f4ba7ba914e20cb913656c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XGPHHQVU76IZ5GI25BM6SHFRMK/bundle.json","state_url":"https://pith.science/pith/XGPHHQVU76IZ5GI25BM6SHFRMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XGPHHQVU76IZ5GI25BM6SHFRMK/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":"2026-06-01T21:58:33Z","links":{"resolver":"https://pith.science/pith/XGPHHQVU76IZ5GI25BM6SHFRMK","bundle":"https://pith.science/pith/XGPHHQVU76IZ5GI25BM6SHFRMK/bundle.json","state":"https://pith.science/pith/XGPHHQVU76IZ5GI25BM6SHFRMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XGPHHQVU76IZ5GI25BM6SHFRMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XGPHHQVU76IZ5GI25BM6SHFRMK","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":"839bcdd902bb727c58bb5c215885357e77c44844a48d13bc70dc8bb640d935e0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-03T23:55:20Z","title_canon_sha256":"744e128f012e858409b15263e070aca2d79ae24a4d37cbd42b11d5c8a6cbb6be"},"schema_version":"1.0","source":{"id":"0902.0646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0646","created_at":"2026-05-18T02:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0646v1","created_at":"2026-05-18T02:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0646","created_at":"2026-05-18T02:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"XGPHHQVU76IZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XGPHHQVU76IZ5GI2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XGPHHQVU","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:05039193a37143af0fd11d0be5aea1aa740bc1c412f4ba7ba914e20cb913656c","target":"graph","created_at":"2026-05-18T02:14:54Z","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 study the dynamics of a molecule's nuclear wave-function near an avoided crossing of two electronic energy levels, for one nuclear degree of freedom. We derive the general form of the Schroedinger equation in the n-th superadiabatic representation for all n, and give some partial results about the asymptotics for large n. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace, when a wave packet crosses the transition region. In the optimal superadiabatic representation, which we define, this c","authors_text":"Benjamin D. Goddard, Stefan Teufel, Volker Betz","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-03T23:55:20Z","title":"Superadiabatic transition histories in quantum molecular dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0646","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":"sha256:3e6280ff10bae6aeb596606bdd8e35e11f5edc8cf22f75a701f0c209aff45387","target":"record","created_at":"2026-05-18T02:14:54Z","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":"839bcdd902bb727c58bb5c215885357e77c44844a48d13bc70dc8bb640d935e0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-03T23:55:20Z","title_canon_sha256":"744e128f012e858409b15263e070aca2d79ae24a4d37cbd42b11d5c8a6cbb6be"},"schema_version":"1.0","source":{"id":"0902.0646","kind":"arxiv","version":1}},"canonical_sha256":"b99e73c2b4ff919e991ae859e91cb1629d6c0bee91b27b415e197a91e9690487","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b99e73c2b4ff919e991ae859e91cb1629d6c0bee91b27b415e197a91e9690487","first_computed_at":"2026-05-18T02:14:54.341345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:54.341345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zky1t4wiBWlkxuz6nImVW/uzcxpMOBj0tBQlaiJwIFPEALYgD+9LUylenShv8t4Z4U1x1PJr/zIhULFlCJeNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:54.341945Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e6280ff10bae6aeb596606bdd8e35e11f5edc8cf22f75a701f0c209aff45387","sha256:05039193a37143af0fd11d0be5aea1aa740bc1c412f4ba7ba914e20cb913656c"],"state_sha256":"b551b456d0cb042ed5e6f24a00d7da94e11f2770f7908a535ca03fed11ccf017"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIsXx/yh2rMCAqADS1iDnNHvF98ik4lh48IC3rlPJIOmWYL2OWL4Ia9rN8+05VTTo7TffGLlAU5XC18hLXocBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:58:33.420035Z","bundle_sha256":"8a83e42d69649cd6d52d234e76efe7c8b1c9ad3392954fc3e0dcefa854a50955"}}