{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E7ISXOT5CRUCERTUB3EVPPL2PP","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":"d2744adeea9caf8ad572b6e951016db54c7f217919950d7b8035a5abc887c7ec","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-08T15:48:11Z","title_canon_sha256":"00a450ec8e02ae9f8012332ff944804a9a810e46cacc3479749e89d356bca86e"},"schema_version":"1.0","source":{"id":"1608.02501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02501","created_at":"2026-05-18T00:49:16Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02501v1","created_at":"2026-05-18T00:49:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02501","created_at":"2026-05-18T00:49:16Z"},{"alias_kind":"pith_short_12","alias_value":"E7ISXOT5CRUC","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E7ISXOT5CRUCERTU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E7ISXOT5","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:868d7690627bb7b8f2d8a064c0f188aecc3e40fdc27e5464727d354251653247","target":"graph","created_at":"2026-05-18T00:49:16Z","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":"As a model for the semiclassical analysis of quantum-mechanical systems with both potentials and boundary conditions, we construct the WKB propagator for a linear potential sloping away from an impenetrable boundary. First, we find all classical paths from point $y$ to point $x$ in time $t$ and calculate the corresponding action and amplitude functions. A large part of space-time turns out to be classically inaccessible, and the boundary of this region is a caustic of an unusual type, where the amplitude vanishes instead of diverging. We show that this curve is the limit of caustics in the usu","authors_text":"S. A. Fulling, T. A. Zapata","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-08T15:48:11Z","title":"WKB propagators in position and momentum space for a linear potential with a \"ceiling\" boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02501","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":"sha256:57413e57af59a07101565973fa64fafe1c607bd9cbc98e07cf6e0a067b64a66f","target":"record","created_at":"2026-05-18T00:49:16Z","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":"d2744adeea9caf8ad572b6e951016db54c7f217919950d7b8035a5abc887c7ec","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-08T15:48:11Z","title_canon_sha256":"00a450ec8e02ae9f8012332ff944804a9a810e46cacc3479749e89d356bca86e"},"schema_version":"1.0","source":{"id":"1608.02501","kind":"arxiv","version":1}},"canonical_sha256":"27d12bba7d14682246740ec957bd7a7bf655331b28bca0bf8d09ea31edeeb38b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27d12bba7d14682246740ec957bd7a7bf655331b28bca0bf8d09ea31edeeb38b","first_computed_at":"2026-05-18T00:49:16.230572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:16.230572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y7lULZY0rit95HJXoGrBJ5aWtvPrapSiyS3+aCY4KUm0ha+mvwGG6+OMAMCEXb3vOkz1ACg4Ki4QXO87Ni9rCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:16.230925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57413e57af59a07101565973fa64fafe1c607bd9cbc98e07cf6e0a067b64a66f","sha256:868d7690627bb7b8f2d8a064c0f188aecc3e40fdc27e5464727d354251653247"],"state_sha256":"2c383b70d0fad3b2fbc58c5ea44873e8203afb73a4c016cddd0e3357afbd4b74"}