{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:D5A3GVWXDG4A7EZ65ATZEFN7JT","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":"1ff3f160fcc32e2fdd08ea532da5ab200c50b77a91bff1c45cc8a9c3d858004a","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-02-19T07:00:01Z","title_canon_sha256":"1406d003a03d5c4232799a65f47fa159e102690879de1d78525615f449aeacb4"},"schema_version":"1.0","source":{"id":"2102.09767","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.09767","created_at":"2026-07-05T04:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"2102.09767v4","created_at":"2026-07-05T04:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.09767","created_at":"2026-07-05T04:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"D5A3GVWXDG4A","created_at":"2026-07-05T04:22:15Z"},{"alias_kind":"pith_short_16","alias_value":"D5A3GVWXDG4A7EZ6","created_at":"2026-07-05T04:22:15Z"},{"alias_kind":"pith_short_8","alias_value":"D5A3GVWX","created_at":"2026-07-05T04:22:15Z"}],"graph_snapshots":[{"event_id":"sha256:7db6bb66bedb3d7422036827c1213f11b87c0266c78c934e2eb384c6ad599b34","target":"graph","created_at":"2026-07-05T04:22:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.09767/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, the Lorentzian path integral formulation using the Picard-Lefschetz theory has attracted much attention in quantum cosmology. In this paper, we analyze the tunneling amplitude in quantum mechanics by using the Lorentzian Picard-Lefschetz formulation and compare it with the WKB analysis of the conventional Schr\\\"{o}dinger equation. We show that the Picard-Lefschetz Lorentzian formulation is consistent with the WKB approximation for wave-function and the Euclidean path integral formulation utilizing the solutions of the Euclidean constraint equation. We also consider some problems of t","authors_text":"Hiroki Matsui","cross_cats":["hep-th","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-02-19T07:00:01Z","title":"Lorentzian path integral for quantum tunneling and WKB approximation for wave-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.09767","kind":"arxiv","version":4},"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":"sha256:4a697b31fd4660f9e434c0289845168cf8527c0d6c847faea968b48cfce6c059","target":"record","created_at":"2026-07-05T04:22:15Z","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":"1ff3f160fcc32e2fdd08ea532da5ab200c50b77a91bff1c45cc8a9c3d858004a","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-02-19T07:00:01Z","title_canon_sha256":"1406d003a03d5c4232799a65f47fa159e102690879de1d78525615f449aeacb4"},"schema_version":"1.0","source":{"id":"2102.09767","kind":"arxiv","version":4}},"canonical_sha256":"1f41b356d719b80f933ee8279215bf4cf638493e218bf58514dd717d98b9bc76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f41b356d719b80f933ee8279215bf4cf638493e218bf58514dd717d98b9bc76","first_computed_at":"2026-07-05T04:22:15.277932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:22:15.277932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSwHa7NNdnXi02epBKqRLLeOScWOYJwefUJEHdjuy6sUGQVFPXmZsQGJ53fRSwbwU4zsYZJzdGB0EaNaMe9mBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:22:15.278424Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.09767","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a697b31fd4660f9e434c0289845168cf8527c0d6c847faea968b48cfce6c059","sha256:7db6bb66bedb3d7422036827c1213f11b87c0266c78c934e2eb384c6ad599b34"],"state_sha256":"d94652bd4f78a0fd462aaa020dfbef785fede79f6c1880d25d1d73d91f4089b2"}