{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:HMDGJIV23PCD57ZM6Q3XJE4GDH","short_pith_number":"pith:HMDGJIV2","canonical_record":{"source":{"id":"quant-ph/0606129","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-06-15T07:00:28Z","cross_cats_sorted":[],"title_canon_sha256":"cc958f25b15efbe366888ab9eef54944aebf37de87ddfb6153f1f30083e9b73a","abstract_canon_sha256":"4bc4068ffabd8ab43a3499c221ebac146842e2f2aa8542aa624c49594bf4197b"},"schema_version":"1.0"},"canonical_sha256":"3b0664a2badbc43eff2cf43774938619c57a71a028862e83106faeed0902b9f6","source":{"kind":"arxiv","id":"quant-ph/0606129","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0606129","created_at":"2026-05-18T01:37:56Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0606129v2","created_at":"2026-05-18T01:37:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0606129","created_at":"2026-05-18T01:37:56Z"},{"alias_kind":"pith_short_12","alias_value":"HMDGJIV23PCD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HMDGJIV23PCD57ZM","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HMDGJIV2","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:HMDGJIV23PCD57ZM6Q3XJE4GDH","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0606129","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-06-15T07:00:28Z","cross_cats_sorted":[],"title_canon_sha256":"cc958f25b15efbe366888ab9eef54944aebf37de87ddfb6153f1f30083e9b73a","abstract_canon_sha256":"4bc4068ffabd8ab43a3499c221ebac146842e2f2aa8542aa624c49594bf4197b"},"schema_version":"1.0"},"canonical_sha256":"3b0664a2badbc43eff2cf43774938619c57a71a028862e83106faeed0902b9f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:56.452002Z","signature_b64":"qqQSE+/EuOrBnXwvFhI2BfqF8MKz1c08WNtuaGn0wdb9Lgr+F8mz9tSTseV+8kGL1iAUJQojEm0PmSdWM7N1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b0664a2badbc43eff2cf43774938619c57a71a028862e83106faeed0902b9f6","last_reissued_at":"2026-05-18T01:37:56.451310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:56.451310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0606129","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":"2026-05-18T01:37:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AcwnOs7aW5stmJD7p8azTOgzPq+XPlkPjn3v7jNncUJfiO4Q+4muHcRmnS8OuNXEG5TlspeJ8DemXIHX12LdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:45:18.464090Z"},"content_sha256":"2309f2d552b128e43ce4f125859c8f59f0e521300bc612ab8b4a8b20fb3fe083","schema_version":"1.0","event_id":"sha256:2309f2d552b128e43ce4f125859c8f59f0e521300bc612ab8b4a8b20fb3fe083"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:HMDGJIV23PCD57ZM6Q3XJE4GDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scattering in PT-symmetric quantum mechanics","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"A. Ventura, F. Cannata, J.-P. Dedonder","submitted_at":"2006-06-15T07:00:28Z","abstract_excerpt":"A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with hermiticity, T invariance and PT invariance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0606129","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":"2026-05-18T01:37:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tgbHDtF3ATlFe5M3M2T5KY2zPIypEUt/fy/RtZfpAkM8srPV1Jd2GVP1Bt/jykLu7LPdPuQ7F/hu9snFRZ8wBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:45:18.464824Z"},"content_sha256":"d44367995d5f85a98dbc7bc3dfa9063e1e45a225a8377e1fc7b9f57ef486ed53","schema_version":"1.0","event_id":"sha256:d44367995d5f85a98dbc7bc3dfa9063e1e45a225a8377e1fc7b9f57ef486ed53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMDGJIV23PCD57ZM6Q3XJE4GDH/bundle.json","state_url":"https://pith.science/pith/HMDGJIV23PCD57ZM6Q3XJE4GDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMDGJIV23PCD57ZM6Q3XJE4GDH/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":"2026-05-26T00:45:18Z","links":{"resolver":"https://pith.science/pith/HMDGJIV23PCD57ZM6Q3XJE4GDH","bundle":"https://pith.science/pith/HMDGJIV23PCD57ZM6Q3XJE4GDH/bundle.json","state":"https://pith.science/pith/HMDGJIV23PCD57ZM6Q3XJE4GDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMDGJIV23PCD57ZM6Q3XJE4GDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:HMDGJIV23PCD57ZM6Q3XJE4GDH","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":"4bc4068ffabd8ab43a3499c221ebac146842e2f2aa8542aa624c49594bf4197b","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-06-15T07:00:28Z","title_canon_sha256":"cc958f25b15efbe366888ab9eef54944aebf37de87ddfb6153f1f30083e9b73a"},"schema_version":"1.0","source":{"id":"quant-ph/0606129","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0606129","created_at":"2026-05-18T01:37:56Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0606129v2","created_at":"2026-05-18T01:37:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0606129","created_at":"2026-05-18T01:37:56Z"},{"alias_kind":"pith_short_12","alias_value":"HMDGJIV23PCD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HMDGJIV23PCD57ZM","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HMDGJIV2","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d44367995d5f85a98dbc7bc3dfa9063e1e45a225a8377e1fc7b9f57ef486ed53","target":"graph","created_at":"2026-05-18T01:37:56Z","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":"A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with hermiticity, T invariance and PT invariance.","authors_text":"A. Ventura, F. Cannata, J.-P. Dedonder","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-06-15T07:00:28Z","title":"Scattering in PT-symmetric quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0606129","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":"sha256:2309f2d552b128e43ce4f125859c8f59f0e521300bc612ab8b4a8b20fb3fe083","target":"record","created_at":"2026-05-18T01:37:56Z","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":"4bc4068ffabd8ab43a3499c221ebac146842e2f2aa8542aa624c49594bf4197b","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-06-15T07:00:28Z","title_canon_sha256":"cc958f25b15efbe366888ab9eef54944aebf37de87ddfb6153f1f30083e9b73a"},"schema_version":"1.0","source":{"id":"quant-ph/0606129","kind":"arxiv","version":2}},"canonical_sha256":"3b0664a2badbc43eff2cf43774938619c57a71a028862e83106faeed0902b9f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b0664a2badbc43eff2cf43774938619c57a71a028862e83106faeed0902b9f6","first_computed_at":"2026-05-18T01:37:56.451310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:56.451310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qqQSE+/EuOrBnXwvFhI2BfqF8MKz1c08WNtuaGn0wdb9Lgr+F8mz9tSTseV+8kGL1iAUJQojEm0PmSdWM7N1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:56.452002Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0606129","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2309f2d552b128e43ce4f125859c8f59f0e521300bc612ab8b4a8b20fb3fe083","sha256:d44367995d5f85a98dbc7bc3dfa9063e1e45a225a8377e1fc7b9f57ef486ed53"],"state_sha256":"78de1eadc8bd1a5d920354584e8475228547ad540934a1225f75fb33f35ef398"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QFn3q7gH4FTHC4C1kuYKfIFtT2ClM7Dx2Eold+rdZmCV+kWez0ZqcdQSKT5xLBbgZxNQSWLIeI3y1fChq5wvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:45:18.468815Z","bundle_sha256":"e99649818a9772baecc701504862be2cfbf9a189d3ef02938be3db159b44ecf8"}}