{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:4KVMAZAFX6N46ARLU2Q52I7S2I","short_pith_number":"pith:4KVMAZAF","canonical_record":{"source":{"id":"2307.03504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-07-07T10:40:20Z","cross_cats_sorted":["math-ph","math.MP","physics.atom-ph"],"title_canon_sha256":"6588ad02e8253cb87b2d5ec61a57c242f80a56460134af14bfedf1aca681db4f","abstract_canon_sha256":"5197bea7c0d446e4b1f7772dec3f47f676c348bc58737908cb755fdb906ec810"},"schema_version":"1.0"},"canonical_sha256":"e2aac06405bf9bcf022ba6a1dd23f2d207610dd61e2b72473abfcb86e420553b","source":{"kind":"arxiv","id":"2307.03504","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.03504","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"2307.03504v3","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.03504","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"4KVMAZAFX6N4","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"pith_short_16","alias_value":"4KVMAZAFX6N46ARL","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"pith_short_8","alias_value":"4KVMAZAF","created_at":"2026-07-05T08:51:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:4KVMAZAFX6N46ARLU2Q52I7S2I","target":"record","payload":{"canonical_record":{"source":{"id":"2307.03504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-07-07T10:40:20Z","cross_cats_sorted":["math-ph","math.MP","physics.atom-ph"],"title_canon_sha256":"6588ad02e8253cb87b2d5ec61a57c242f80a56460134af14bfedf1aca681db4f","abstract_canon_sha256":"5197bea7c0d446e4b1f7772dec3f47f676c348bc58737908cb755fdb906ec810"},"schema_version":"1.0"},"canonical_sha256":"e2aac06405bf9bcf022ba6a1dd23f2d207610dd61e2b72473abfcb86e420553b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:51:42.531841Z","signature_b64":"YcyF+BIf5fpouThiPTv99CMObYXnM4gNtYMZAGlW15K3/kNPwzJ906TcVdcNSQBVBmbe70Tf8L7mNiYNX2cTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2aac06405bf9bcf022ba6a1dd23f2d207610dd61e2b72473abfcb86e420553b","last_reissued_at":"2026-07-05T08:51:42.531296Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:51:42.531296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.03504","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"olP//tZRb/UAnJQ1olIPsBdQn+OVR434wlY0FAkYiSDhQGnyizYRy2dHY6rW5GwSb/UmInRZY02BS0y49gz4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:54:20.043245Z"},"content_sha256":"2d374b1e36903a4a3fdf73a7b2b6a81f66e86ffc23e4cd422de2214d74979c14","schema_version":"1.0","event_id":"sha256:2d374b1e36903a4a3fdf73a7b2b6a81f66e86ffc23e4cd422de2214d74979c14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:4KVMAZAFX6N46ARLU2Q52I7S2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact WKB Analysis and TBA Equations for the Stark Effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.atom-ph"],"primary_cat":"hep-th","authors_text":"Jingjing Yang, Katsushi Ito","submitted_at":"2023-07-07T10:40:20Z","abstract_excerpt":"We apply the exact WKB analysis to a couple of one-dimensional Schroedinger-type equations reduced from the Stark effect of hydrogen in a uniform electric field. By introducing Langer's modification and incorporating the Stokes graphs, we prove the exactness of the Bohr-Sommerfeld quantization conditions for the Borel-resummed quantum WKB periods in the specific parameter regions of the electric field intensity and magnetic quantum number. It is also found these quantization conditions get modified with an additional suppressed contribution when the parameters vary beyond the specific regions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.03504","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.03504/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1sZXkpXJeNXqhNIi7Yyyfp+qirxz7mvMKYI8y0/pOqngytsGIGHvct+/vlfiYwUad2di6+yx3pmR/JV5EsE0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:54:20.044171Z"},"content_sha256":"31e57241e67294c804e85fdc3d6355c6f312497aa39f5c382bcb101535cd4d6c","schema_version":"1.0","event_id":"sha256:31e57241e67294c804e85fdc3d6355c6f312497aa39f5c382bcb101535cd4d6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KVMAZAFX6N46ARLU2Q52I7S2I/bundle.json","state_url":"https://pith.science/pith/4KVMAZAFX6N46ARLU2Q52I7S2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KVMAZAFX6N46ARLU2Q52I7S2I/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":"2026-08-07T23:54:20Z","links":{"resolver":"https://pith.science/pith/4KVMAZAFX6N46ARLU2Q52I7S2I","bundle":"https://pith.science/pith/4KVMAZAFX6N46ARLU2Q52I7S2I/bundle.json","state":"https://pith.science/pith/4KVMAZAFX6N46ARLU2Q52I7S2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KVMAZAFX6N46ARLU2Q52I7S2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:4KVMAZAFX6N46ARLU2Q52I7S2I","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":"5197bea7c0d446e4b1f7772dec3f47f676c348bc58737908cb755fdb906ec810","cross_cats_sorted":["math-ph","math.MP","physics.atom-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-07-07T10:40:20Z","title_canon_sha256":"6588ad02e8253cb87b2d5ec61a57c242f80a56460134af14bfedf1aca681db4f"},"schema_version":"1.0","source":{"id":"2307.03504","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.03504","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"2307.03504v3","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.03504","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"4KVMAZAFX6N4","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"pith_short_16","alias_value":"4KVMAZAFX6N46ARL","created_at":"2026-07-05T08:51:42Z"},{"alias_kind":"pith_short_8","alias_value":"4KVMAZAF","created_at":"2026-07-05T08:51:42Z"}],"graph_snapshots":[{"event_id":"sha256:31e57241e67294c804e85fdc3d6355c6f312497aa39f5c382bcb101535cd4d6c","target":"graph","created_at":"2026-07-05T08:51:42Z","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/2307.03504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We apply the exact WKB analysis to a couple of one-dimensional Schroedinger-type equations reduced from the Stark effect of hydrogen in a uniform electric field. By introducing Langer's modification and incorporating the Stokes graphs, we prove the exactness of the Bohr-Sommerfeld quantization conditions for the Borel-resummed quantum WKB periods in the specific parameter regions of the electric field intensity and magnetic quantum number. It is also found these quantization conditions get modified with an additional suppressed contribution when the parameters vary beyond the specific regions.","authors_text":"Jingjing Yang, Katsushi Ito","cross_cats":["math-ph","math.MP","physics.atom-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-07-07T10:40:20Z","title":"Exact WKB Analysis and TBA Equations for the Stark Effect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.03504","kind":"arxiv","version":3},"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":"sha256:2d374b1e36903a4a3fdf73a7b2b6a81f66e86ffc23e4cd422de2214d74979c14","target":"record","created_at":"2026-07-05T08:51:42Z","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":"5197bea7c0d446e4b1f7772dec3f47f676c348bc58737908cb755fdb906ec810","cross_cats_sorted":["math-ph","math.MP","physics.atom-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-07-07T10:40:20Z","title_canon_sha256":"6588ad02e8253cb87b2d5ec61a57c242f80a56460134af14bfedf1aca681db4f"},"schema_version":"1.0","source":{"id":"2307.03504","kind":"arxiv","version":3}},"canonical_sha256":"e2aac06405bf9bcf022ba6a1dd23f2d207610dd61e2b72473abfcb86e420553b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2aac06405bf9bcf022ba6a1dd23f2d207610dd61e2b72473abfcb86e420553b","first_computed_at":"2026-07-05T08:51:42.531296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:51:42.531296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YcyF+BIf5fpouThiPTv99CMObYXnM4gNtYMZAGlW15K3/kNPwzJ906TcVdcNSQBVBmbe70Tf8L7mNiYNX2cTBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:51:42.531841Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.03504","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d374b1e36903a4a3fdf73a7b2b6a81f66e86ffc23e4cd422de2214d74979c14","sha256:31e57241e67294c804e85fdc3d6355c6f312497aa39f5c382bcb101535cd4d6c"],"state_sha256":"86d9f9b7e17a834d2cbebb253682d07906d496ccc398f989dfb5efe6ac0535aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RjDPcDzm8P++tHLvGkLJETnhEdNmX0rb8fVleqqTQhC6odrFAxN6oRlAEnyy1oHF8IoQdnLe2O8Un9WNZrr2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T23:54:20.050419Z","bundle_sha256":"104f3f0f769e7ae7c4ee94acda7e0e827c71a8572cf8522a4d63c643b4f12047"}}