{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JOIL2FTG333V4J7RBX57AR3SIH","short_pith_number":"pith:JOIL2FTG","schema_version":"1.0","canonical_sha256":"4b90bd1666def75e27f10dfbf0477241d8dfa8c9a378c5f6c5de88e5db34c0de","source":{"kind":"arxiv","id":"1402.3816","version":1},"attestation_state":"computed","paper":{"title":"Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander V Turbiner, jr, Willard Miller","submitted_at":"2014-02-16T16:58:55Z","abstract_excerpt":"We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We give the details of the Hamiltonian reduction of the 3D system to a 2D system with modified potential that is separable in elliptic coordinates. The potentials for which there is double-periodicity of the Schr\\\"odinger operator in the space of prolate spheroidal coordinates, including one for the H$_2^+$ molecular ion, are indicated. We study possible potentia"},"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":"1402.3816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-16T16:58:55Z","cross_cats_sorted":["math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"0caab98893b7a7d99cd487415b5c900b10273e44ce78da25dfa44506c1373128","abstract_canon_sha256":"a43fbb3a77e6c79dd60aca09bf4ddb3a13ada92ce7882c53b787c2d3ac5e3979"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:43.996351Z","signature_b64":"EZ+EUbkRK1+RC2YfhfNnvEDMNuk1pBC30daH+ioybYyXDzCb6BM2+XOhZy0ks7ghjv2KnaBFfFkO28ttsej5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b90bd1666def75e27f10dfbf0477241d8dfa8c9a378c5f6c5de88e5db34c0de","last_reissued_at":"2026-05-18T01:11:43.995891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:43.995891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Particle in a field of two centers in prolate spheroidal coordinates: integrability and solvability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexander V Turbiner, jr, Willard Miller","submitted_at":"2014-02-16T16:58:55Z","abstract_excerpt":"We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We give the details of the Hamiltonian reduction of the 3D system to a 2D system with modified potential that is separable in elliptic coordinates. The potentials for which there is double-periodicity of the Schr\\\"odinger operator in the space of prolate spheroidal coordinates, including one for the H$_2^+$ molecular ion, are indicated. We study possible potentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3816","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":"1402.3816","created_at":"2026-05-18T01:11:43.995953+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.3816v1","created_at":"2026-05-18T01:11:43.995953+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3816","created_at":"2026-05-18T01:11:43.995953+00:00"},{"alias_kind":"pith_short_12","alias_value":"JOIL2FTG333V","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JOIL2FTG333V4J7R","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JOIL2FTG","created_at":"2026-05-18T12:28:35.611951+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/JOIL2FTG333V4J7RBX57AR3SIH","json":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH.json","graph_json":"https://pith.science/api/pith-number/JOIL2FTG333V4J7RBX57AR3SIH/graph.json","events_json":"https://pith.science/api/pith-number/JOIL2FTG333V4J7RBX57AR3SIH/events.json","paper":"https://pith.science/paper/JOIL2FTG"},"agent_actions":{"view_html":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH","download_json":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH.json","view_paper":"https://pith.science/paper/JOIL2FTG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.3816&json=true","fetch_graph":"https://pith.science/api/pith-number/JOIL2FTG333V4J7RBX57AR3SIH/graph.json","fetch_events":"https://pith.science/api/pith-number/JOIL2FTG333V4J7RBX57AR3SIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/action/storage_attestation","attest_author":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/action/author_attestation","sign_citation":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/action/citation_signature","submit_replication":"https://pith.science/pith/JOIL2FTG333V4J7RBX57AR3SIH/action/replication_record"}},"created_at":"2026-05-18T01:11:43.995953+00:00","updated_at":"2026-05-18T01:11:43.995953+00:00"}