{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7TSFIMA2JMWXTCOCZ3HBZWY6DD","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":"b3cd98708e2066a8bc69876218c8e7bf4b758e180b77e6ed9b9c00a940fc0c6b","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-26T10:13:05Z","title_canon_sha256":"a6b745184e3b854b5b18351df722bcac4d0b72fbaffbc68d9c3af659830c48f4"},"schema_version":"1.0","source":{"id":"1112.5829","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5829","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5829v1","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5829","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"7TSFIMA2JMWX","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7TSFIMA2JMWXTCOC","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7TSFIMA2","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:446733b0dab829fdf21ff87c677d9476b34390041c027e52fea89cafe28d4392","target":"graph","created_at":"2026-05-18T04:05:37Z","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 one-dimensional Schr\\\"odinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite intervals. We also discuss the relation between our results and the WKB approximation.","authors_text":"Toru Miyazawa","cross_cats":["cond-mat.stat-mech","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-26T10:13:05Z","title":"Expressions of the Green function in terms of reflection coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5829","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":"sha256:1c603a80e56947a0d9aee078ab0a091d2d2600209a1e3d534e89c549ff0c22bb","target":"record","created_at":"2026-05-18T04:05:37Z","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":"b3cd98708e2066a8bc69876218c8e7bf4b758e180b77e6ed9b9c00a940fc0c6b","cross_cats_sorted":["cond-mat.stat-mech","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-26T10:13:05Z","title_canon_sha256":"a6b745184e3b854b5b18351df722bcac4d0b72fbaffbc68d9c3af659830c48f4"},"schema_version":"1.0","source":{"id":"1112.5829","kind":"arxiv","version":1}},"canonical_sha256":"fce454301a4b2d7989c2cece1cdb1e18fc67aca37d8fc08a7d33f6d4710f05e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fce454301a4b2d7989c2cece1cdb1e18fc67aca37d8fc08a7d33f6d4710f05e4","first_computed_at":"2026-05-18T04:05:37.524551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:37.524551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ag5KWMW6MANn0bnmlrGIoDxOMK8a/TSvroBN+Fda/yadGW3IAHzN/KjAGkdrYuYvDQCpYpb6IJ97o7yFZCkcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:37.525200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5829","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c603a80e56947a0d9aee078ab0a091d2d2600209a1e3d534e89c549ff0c22bb","sha256:446733b0dab829fdf21ff87c677d9476b34390041c027e52fea89cafe28d4392"],"state_sha256":"49bbc2293efaebb39c7a82821b6aa4240f73a754cc2999a3b0127f983bf6dc87"}