{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:U5SGO7SXQDTZHY5LLPOYTG7WZI","short_pith_number":"pith:U5SGO7SX","schema_version":"1.0","canonical_sha256":"a764677e5780e793e3ab5bdd899bf6ca214199bff61ac377df1f8165d919bc45","source":{"kind":"arxiv","id":"0912.4659","version":2},"attestation_state":"computed","paper":{"title":"Probability Density in the Complex Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Carl M. Bender, Daniel W. Hook, Peter N. Meisinger, Qing-hai Wang","submitted_at":"2009-12-23T15:03:10Z","abstract_excerpt":"The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density $\\rho(z)$ in the complex plane. It is shown that there exist infinitely many complex contours $C$ of infinite length on"},"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":"0912.4659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-12-23T15:03:10Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"63327c8dd55b955151a44f67deaca610f1b5cc435f41d8fbd85d27d25d9d41e8","abstract_canon_sha256":"cc818f7967b77e2264f8c70eac1f7420b5841a502e68336cd3e2d677c55dfbed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:55.521338Z","signature_b64":"pO5qesHJdb5f+kOI8AhhpLwPCzmi2TB/I8eC1poQhf+TJa1jkI9cVFNSRbUu+FexVOgL5voxivFMiVB5oGKhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a764677e5780e793e3ab5bdd899bf6ca214199bff61ac377df1f8165d919bc45","last_reissued_at":"2026-05-18T02:33:55.520946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:55.520946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probability Density in the Complex Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"Carl M. Bender, Daniel W. Hook, Peter N. Meisinger, Qing-hai Wang","submitted_at":"2009-12-23T15:03:10Z","abstract_excerpt":"The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density $\\rho(z)$ in the complex plane. It is shown that there exist infinitely many complex contours $C$ of infinite length on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4659","kind":"arxiv","version":2},"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":"0912.4659","created_at":"2026-05-18T02:33:55.521002+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.4659v2","created_at":"2026-05-18T02:33:55.521002+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4659","created_at":"2026-05-18T02:33:55.521002+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5SGO7SXQDTZ","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5SGO7SXQDTZHY5L","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5SGO7SX","created_at":"2026-05-18T12:26:02.257875+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/U5SGO7SXQDTZHY5LLPOYTG7WZI","json":"https://pith.science/pith/U5SGO7SXQDTZHY5LLPOYTG7WZI.json","graph_json":"https://pith.science/api/pith-number/U5SGO7SXQDTZHY5LLPOYTG7WZI/graph.json","events_json":"https://pith.science/api/pith-number/U5SGO7SXQDTZHY5LLPOYTG7WZI/events.json","paper":"https://pith.science/paper/U5SGO7SX"},"agent_actions":{"view_html":"https://pith.science/pith/U5SGO7SXQDTZHY5LLPOYTG7WZI","download_json":"https://pith.science/pith/U5SGO7SXQDTZHY5LLPOYTG7WZI.json","view_paper":"https://pith.science/paper/U5SGO7SX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.4659&json=true","fetch_graph":"https://pith.science/api/pith-number/U5SGO7SXQDTZHY5LLPOYTG7WZI/graph.json","fetch_events":"https://pith.science/api/pith-number/U5SGO7SXQDTZHY5LLPOYTG7WZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5SGO7SXQDTZHY5LLPOYTG7WZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5SGO7SXQDTZHY5LLPOYTG7WZI/action/storage_attestation","attest_author":"https://pith.science/pith/U5SGO7SXQDTZHY5LLPOYTG7WZI/action/author_attestation","sign_citation":"https://pith.science/pith/U5SGO7SXQDTZHY5LLPOYTG7WZI/action/citation_signature","submit_replication":"https://pith.science/pith/U5SGO7SXQDTZHY5LLPOYTG7WZI/action/replication_record"}},"created_at":"2026-05-18T02:33:55.521002+00:00","updated_at":"2026-05-18T02:33:55.521002+00:00"}