{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4RLHHFIZXPDGV7S6PYUSQL5K6U","short_pith_number":"pith:4RLHHFIZ","schema_version":"1.0","canonical_sha256":"e456739519bbc66afe5e7e29282faaf50ea54874f464e20b09a95c8ff240d71c","source":{"kind":"arxiv","id":"1312.5117","version":1},"attestation_state":"computed","paper":{"title":"Comparison of two semiclassical expansions for a family of PT-symmetric oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Francisco M. Fern\\'andez, Javier Garcia","submitted_at":"2013-12-18T12:44:33Z","abstract_excerpt":"We show that a recently developed semiclassical expansion for the eigenvalues of PT-symmetric oscillators of the form $V(x)=(ix)^{2N+1}+bix$ does not agree with an earlier WKB expression for $V(x)=-(ix)^{2N+1}$ the case $b=0$. The reason is due to the choice of different paths in the complex plane for the calculation of the WKB integrals. We compare the Stokes and anti-Stokes lines that apply to each case for the quintic oscillator and derive a general WKB expression that contains the two earlier ones."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.5117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-18T12:44:33Z","cross_cats_sorted":[],"title_canon_sha256":"303f088865e9e920c923ff4ce417d7087cdd5601c2aca9fed46861cc115de220","abstract_canon_sha256":"0e39aa30039774e0b8af0970b141b537184bc6f86b9eff967b97627dd0ca84c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:16.218257Z","signature_b64":"Cu/8zBlT89wwJcXVMqnsHIyBReT/VQggZWA0OFuII5asPBdnARvDOlIbdhLbm0d0ZA7VlZOCCQ5cteEDhDW/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e456739519bbc66afe5e7e29282faaf50ea54874f464e20b09a95c8ff240d71c","last_reissued_at":"2026-05-18T03:04:16.217588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:16.217588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparison of two semiclassical expansions for a family of PT-symmetric oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Francisco M. Fern\\'andez, Javier Garcia","submitted_at":"2013-12-18T12:44:33Z","abstract_excerpt":"We show that a recently developed semiclassical expansion for the eigenvalues of PT-symmetric oscillators of the form $V(x)=(ix)^{2N+1}+bix$ does not agree with an earlier WKB expression for $V(x)=-(ix)^{2N+1}$ the case $b=0$. The reason is due to the choice of different paths in the complex plane for the calculation of the WKB integrals. We compare the Stokes and anti-Stokes lines that apply to each case for the quintic oscillator and derive a general WKB expression that contains the two earlier ones."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5117","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1312.5117","created_at":"2026-05-18T03:04:16.217695+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.5117v1","created_at":"2026-05-18T03:04:16.217695+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5117","created_at":"2026-05-18T03:04:16.217695+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RLHHFIZXPDG","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RLHHFIZXPDGV7S6","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RLHHFIZ","created_at":"2026-05-18T12:27:34.582898+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U","json":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U.json","graph_json":"https://pith.science/api/pith-number/4RLHHFIZXPDGV7S6PYUSQL5K6U/graph.json","events_json":"https://pith.science/api/pith-number/4RLHHFIZXPDGV7S6PYUSQL5K6U/events.json","paper":"https://pith.science/paper/4RLHHFIZ"},"agent_actions":{"view_html":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U","download_json":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U.json","view_paper":"https://pith.science/paper/4RLHHFIZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.5117&json=true","fetch_graph":"https://pith.science/api/pith-number/4RLHHFIZXPDGV7S6PYUSQL5K6U/graph.json","fetch_events":"https://pith.science/api/pith-number/4RLHHFIZXPDGV7S6PYUSQL5K6U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U/action/storage_attestation","attest_author":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U/action/author_attestation","sign_citation":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U/action/citation_signature","submit_replication":"https://pith.science/pith/4RLHHFIZXPDGV7S6PYUSQL5K6U/action/replication_record"}},"created_at":"2026-05-18T03:04:16.217695+00:00","updated_at":"2026-05-18T03:04:16.217695+00:00"}