{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DPPU2HX26JPAGZNRQ4TIUYOEYK","short_pith_number":"pith:DPPU2HX2","canonical_record":{"source":{"id":"1003.4129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-22T11:05:07Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"cb3a33c4e2b7e0db253d52c4d5dce203c7af046d63e141931fe5948cf60ca3af","abstract_canon_sha256":"253f59ccbadb3b6f968db8f20f684e0cec1946c8d9d7c2bd5e0b63cebb1065ae"},"schema_version":"1.0"},"canonical_sha256":"1bdf4d1efaf25e0365b187268a61c4c2bd3be9889cf172ea343a00928fbe2a4b","source":{"kind":"arxiv","id":"1003.4129","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4129","created_at":"2026-05-18T02:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4129v1","created_at":"2026-05-18T02:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4129","created_at":"2026-05-18T02:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"DPPU2HX26JPA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DPPU2HX26JPAGZNR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DPPU2HX2","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DPPU2HX26JPAGZNRQ4TIUYOEYK","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-22T11:05:07Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"cb3a33c4e2b7e0db253d52c4d5dce203c7af046d63e141931fe5948cf60ca3af","abstract_canon_sha256":"253f59ccbadb3b6f968db8f20f684e0cec1946c8d9d7c2bd5e0b63cebb1065ae"},"schema_version":"1.0"},"canonical_sha256":"1bdf4d1efaf25e0365b187268a61c4c2bd3be9889cf172ea343a00928fbe2a4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:24.704746Z","signature_b64":"C4dtXhIHimFnR8Syt7EV1LjdnSvQIrCe4qu+G2bkjfEotumhWDc+iHJHIHzN3qYRBmfyEIJlI4GJdxqcCQChCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bdf4d1efaf25e0365b187268a61c4c2bd3be9889cf172ea343a00928fbe2a4b","last_reissued_at":"2026-05-18T02:08:24.704046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:24.704046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4129","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":"2026-05-18T02:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSrUJPEWybX3k6bLPfuQtHaHFQOO2/I3G4jfVdL/EFBPls1zEN+NWBmaMxjIa5O8gg1tMXYSUIZEbRhiEi3IBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:18:28.859498Z"},"content_sha256":"cf5c5041f4b51de3c81074b9d25c85e342e426f7a7b452a75745b8d791d5ec7a","schema_version":"1.0","event_id":"sha256:cf5c5041f4b51de3c81074b9d25c85e342e426f7a7b452a75745b8d791d5ec7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DPPU2HX26JPAGZNRQ4TIUYOEYK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Expansion for the Wave Function in a one-dimensional Model of Inelastic Interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alessandro Teta, Domenico Finco","submitted_at":"2010-03-22T11:05:07Z","abstract_excerpt":"We consider a two-body quantum system in dimension one composed by a test particle interacting with an harmonic oscillator placed at the position $a>0$. At time zero the test particle is concentrated around the position $R_0$ with average velocity $\\pm v_0$ while the oscillator is in its ground state. In a suitable scaling limit, corresponding for the test particle to a semi-classical regime with small energy exchange with the oscillator, we give a complete asymptotic expansion of the wave function of the system in both cases $R_0 <a$ and $R_0 >a$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4129","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":"2026-05-18T02:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Me/hc6VG2dCeQAKCgN3OWqvfop4txwkDyfJCptmexQzMCMzCGKJNbVCugvrQklUb6CdWgQtRtyduuIyXUT+eAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:18:28.860178Z"},"content_sha256":"ee5bcd00f8a067c68189d6a5e9575c1ce53cdce8510e512c62f5802ac15f3eea","schema_version":"1.0","event_id":"sha256:ee5bcd00f8a067c68189d6a5e9575c1ce53cdce8510e512c62f5802ac15f3eea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPPU2HX26JPAGZNRQ4TIUYOEYK/bundle.json","state_url":"https://pith.science/pith/DPPU2HX26JPAGZNRQ4TIUYOEYK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPPU2HX26JPAGZNRQ4TIUYOEYK/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":"2026-06-08T16:18:28Z","links":{"resolver":"https://pith.science/pith/DPPU2HX26JPAGZNRQ4TIUYOEYK","bundle":"https://pith.science/pith/DPPU2HX26JPAGZNRQ4TIUYOEYK/bundle.json","state":"https://pith.science/pith/DPPU2HX26JPAGZNRQ4TIUYOEYK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPPU2HX26JPAGZNRQ4TIUYOEYK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DPPU2HX26JPAGZNRQ4TIUYOEYK","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":"253f59ccbadb3b6f968db8f20f684e0cec1946c8d9d7c2bd5e0b63cebb1065ae","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-22T11:05:07Z","title_canon_sha256":"cb3a33c4e2b7e0db253d52c4d5dce203c7af046d63e141931fe5948cf60ca3af"},"schema_version":"1.0","source":{"id":"1003.4129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4129","created_at":"2026-05-18T02:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4129v1","created_at":"2026-05-18T02:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4129","created_at":"2026-05-18T02:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"DPPU2HX26JPA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DPPU2HX26JPAGZNR","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DPPU2HX2","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:ee5bcd00f8a067c68189d6a5e9575c1ce53cdce8510e512c62f5802ac15f3eea","target":"graph","created_at":"2026-05-18T02:08:24Z","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 consider a two-body quantum system in dimension one composed by a test particle interacting with an harmonic oscillator placed at the position $a>0$. At time zero the test particle is concentrated around the position $R_0$ with average velocity $\\pm v_0$ while the oscillator is in its ground state. In a suitable scaling limit, corresponding for the test particle to a semi-classical regime with small energy exchange with the oscillator, we give a complete asymptotic expansion of the wave function of the system in both cases $R_0 <a$ and $R_0 >a$.","authors_text":"Alessandro Teta, Domenico Finco","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-22T11:05:07Z","title":"Asymptotic Expansion for the Wave Function in a one-dimensional Model of Inelastic Interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4129","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:cf5c5041f4b51de3c81074b9d25c85e342e426f7a7b452a75745b8d791d5ec7a","target":"record","created_at":"2026-05-18T02:08:24Z","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":"253f59ccbadb3b6f968db8f20f684e0cec1946c8d9d7c2bd5e0b63cebb1065ae","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-22T11:05:07Z","title_canon_sha256":"cb3a33c4e2b7e0db253d52c4d5dce203c7af046d63e141931fe5948cf60ca3af"},"schema_version":"1.0","source":{"id":"1003.4129","kind":"arxiv","version":1}},"canonical_sha256":"1bdf4d1efaf25e0365b187268a61c4c2bd3be9889cf172ea343a00928fbe2a4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bdf4d1efaf25e0365b187268a61c4c2bd3be9889cf172ea343a00928fbe2a4b","first_computed_at":"2026-05-18T02:08:24.704046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:24.704046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C4dtXhIHimFnR8Syt7EV1LjdnSvQIrCe4qu+G2bkjfEotumhWDc+iHJHIHzN3qYRBmfyEIJlI4GJdxqcCQChCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:24.704746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf5c5041f4b51de3c81074b9d25c85e342e426f7a7b452a75745b8d791d5ec7a","sha256:ee5bcd00f8a067c68189d6a5e9575c1ce53cdce8510e512c62f5802ac15f3eea"],"state_sha256":"bb98a4b1334097ef57d5727224d6b354cf3337f33fec3f5bb460651d6907b700"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EX9Bk/1W8Bf/W+rkZQ7EgY5jfHyDXaxBpW7D0Dh765+GaH4xh5OwXlHiP7oZNqHleVKixy8kSnqNHmFXty3HCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:18:28.864458Z","bundle_sha256":"7365b5f76f57fd06b626b7e7f795abf65d32561dd90518bb96cd91e0ae8422f0"}}