{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HWNQIJKKLHZWHAW6BHWPFHM7KZ","short_pith_number":"pith:HWNQIJKK","canonical_record":{"source":{"id":"1004.5017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T12:52:33Z","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph"],"title_canon_sha256":"cf0ea21eb15cff11f5a3c71bca79b1ae70e5fdf7eef23e49c4da96d0fcb93222","abstract_canon_sha256":"716e0780538447eccf2ebdd604a20237ba4770ed36fd944f72e3b7c9569f77db"},"schema_version":"1.0"},"canonical_sha256":"3d9b04254a59f36382de09ecf29d9f564c4b2310435017fe3db278858882532e","source":{"kind":"arxiv","id":"1004.5017","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5017","created_at":"2026-05-18T04:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5017v1","created_at":"2026-05-18T04:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5017","created_at":"2026-05-18T04:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"HWNQIJKKLHZW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HWNQIJKKLHZWHAW6","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HWNQIJKK","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HWNQIJKKLHZWHAW6BHWPFHM7KZ","target":"record","payload":{"canonical_record":{"source":{"id":"1004.5017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T12:52:33Z","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph"],"title_canon_sha256":"cf0ea21eb15cff11f5a3c71bca79b1ae70e5fdf7eef23e49c4da96d0fcb93222","abstract_canon_sha256":"716e0780538447eccf2ebdd604a20237ba4770ed36fd944f72e3b7c9569f77db"},"schema_version":"1.0"},"canonical_sha256":"3d9b04254a59f36382de09ecf29d9f564c4b2310435017fe3db278858882532e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:19.483745Z","signature_b64":"02Uv4Os3Y1ltOeOLYlYm77e8jJx5GSqcyIOFvhOD9QjWwmPx2kJjzqTfQB2WyRLXymirRKnmP1F9Zpdlh3GLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d9b04254a59f36382de09ecf29d9f564c4b2310435017fe3db278858882532e","last_reissued_at":"2026-05-18T04:39:19.483245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:19.483245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.5017","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":"2026-05-18T04:39:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5QZdL3FyotEty5HKRHkSQBYoZh/mz00zk7L9ikwSUkwMJ69g21ghiwRwlwBkXsbKGhbHxWZcdup9eER3vcsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:30:27.230526Z"},"content_sha256":"3263ed5f324df5ef1e0fc4c4ee5df29323a9c3885076e39c8a1fcbfef7ed9930","schema_version":"1.0","event_id":"sha256:3263ed5f324df5ef1e0fc4c4ee5df29323a9c3885076e39c8a1fcbfef7ed9930"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HWNQIJKKLHZWHAW6BHWPFHM7KZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Theory of Reactive Scattering in Phase Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Arseni Goussev, Holger Waalkens, Roman Schubert, Stephen Wiggins","submitted_at":"2010-04-28T12:52:33Z","abstract_excerpt":"We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory.  Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of phase space structure, a {\\em normally hyperbolic invariant manifold} (or, NHIM) is the \"anchor\" on which t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5017","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":"2026-05-18T04:39:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JIKAhdMSMDFDfYC5ZWXr6WgJFCz0HrxbtB8t3Pe7gKY6cX9L4nzRdMLTmmiczTuP9Za9X1UP0ie/RHeQ6XdEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:30:27.230876Z"},"content_sha256":"acbeb5ae275f069ae91f1ea2419395fbdf9d7a9d8047d87d7be7e93b33fe8fd7","schema_version":"1.0","event_id":"sha256:acbeb5ae275f069ae91f1ea2419395fbdf9d7a9d8047d87d7be7e93b33fe8fd7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWNQIJKKLHZWHAW6BHWPFHM7KZ/bundle.json","state_url":"https://pith.science/pith/HWNQIJKKLHZWHAW6BHWPFHM7KZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWNQIJKKLHZWHAW6BHWPFHM7KZ/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":"2026-05-28T13:30:27Z","links":{"resolver":"https://pith.science/pith/HWNQIJKKLHZWHAW6BHWPFHM7KZ","bundle":"https://pith.science/pith/HWNQIJKKLHZWHAW6BHWPFHM7KZ/bundle.json","state":"https://pith.science/pith/HWNQIJKKLHZWHAW6BHWPFHM7KZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWNQIJKKLHZWHAW6BHWPFHM7KZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HWNQIJKKLHZWHAW6BHWPFHM7KZ","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":"716e0780538447eccf2ebdd604a20237ba4770ed36fd944f72e3b7c9569f77db","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T12:52:33Z","title_canon_sha256":"cf0ea21eb15cff11f5a3c71bca79b1ae70e5fdf7eef23e49c4da96d0fcb93222"},"schema_version":"1.0","source":{"id":"1004.5017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5017","created_at":"2026-05-18T04:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5017v1","created_at":"2026-05-18T04:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5017","created_at":"2026-05-18T04:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"HWNQIJKKLHZW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HWNQIJKKLHZWHAW6","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HWNQIJKK","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:acbeb5ae275f069ae91f1ea2419395fbdf9d7a9d8047d87d7be7e93b33fe8fd7","target":"graph","created_at":"2026-05-18T04:39:19Z","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 review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory.  Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of phase space structure, a {\\em normally hyperbolic invariant manifold} (or, NHIM) is the \"anchor\" on which t","authors_text":"Arseni Goussev, Holger Waalkens, Roman Schubert, Stephen Wiggins","cross_cats":["math-ph","math.MP","physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T12:52:33Z","title":"Quantum Theory of Reactive Scattering in Phase Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5017","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":"sha256:3263ed5f324df5ef1e0fc4c4ee5df29323a9c3885076e39c8a1fcbfef7ed9930","target":"record","created_at":"2026-05-18T04:39:19Z","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":"716e0780538447eccf2ebdd604a20237ba4770ed36fd944f72e3b7c9569f77db","cross_cats_sorted":["math-ph","math.MP","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T12:52:33Z","title_canon_sha256":"cf0ea21eb15cff11f5a3c71bca79b1ae70e5fdf7eef23e49c4da96d0fcb93222"},"schema_version":"1.0","source":{"id":"1004.5017","kind":"arxiv","version":1}},"canonical_sha256":"3d9b04254a59f36382de09ecf29d9f564c4b2310435017fe3db278858882532e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d9b04254a59f36382de09ecf29d9f564c4b2310435017fe3db278858882532e","first_computed_at":"2026-05-18T04:39:19.483245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:19.483245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"02Uv4Os3Y1ltOeOLYlYm77e8jJx5GSqcyIOFvhOD9QjWwmPx2kJjzqTfQB2WyRLXymirRKnmP1F9Zpdlh3GLBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:19.483745Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3263ed5f324df5ef1e0fc4c4ee5df29323a9c3885076e39c8a1fcbfef7ed9930","sha256:acbeb5ae275f069ae91f1ea2419395fbdf9d7a9d8047d87d7be7e93b33fe8fd7"],"state_sha256":"9ec967abcd8df2b2119113135f28b292b5ca67f8b0e02e1a817179b95de18991"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bUHdXg2YtkqoccRKaGSeWQRM43hKn5pu8N3Jon8j7kesyB+bKl6hz9Pty/+0DlEtyj5YIIXIPFJVtuwxUKDPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:30:27.232857Z","bundle_sha256":"439447c3a3f31a7bc5aea35287b4aac53699aa7a2554c4ec65181c22c0b3c3bd"}}