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Koepf (Eds.), Orthogonal Polynomials, Springer In","work_id":"","year":2020},{"cited_arxiv_id":"","doi":"10.1007/s10773-008-9806-y","is_internal_anchor":false,"ref_index":5,"title":"C. Tezcan, R. Sever, A general approach for the exact solution of the Schrödinger equation, Int. J. Theor. Phys. 48 (2009) 337–350. doi:10.1007/s10773-008-9806-y. 17","work_id":"7c88d391-a59b-4f3f-b575-712afccb43d9","year":2009}],"snapshot_sha256":"75be49dfa22f3d56f1994657877576143fc7407ed6b0090f0eccd9f9240bc577"},"source":{"id":"2604.27522","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-07T08:54:08.240618Z","id":"11c8855a-d275-48d1-a537-96e8d5f2e893","model_set":{"reader":"grok-4.3"},"one_line_summary":"The extended Nikiforov-Uvarov method applied to the Heun equation from the Pauli equation in constant-curvature spaces produces a quantization condition but cannot satisfy the requirements for polynomial solutions, indicating limited applicability.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The extended Nikiforov-Uvarov method cannot produce polynomial solutions for the Heun equation in the non-relativistic limit of the Dirac equation on curved spaces.","strongest_claim":"the necessary conditions for the existence of polynomial solutions cannot be met, and this fact undermines the reliability of the results obtained. This circumstance forces us to conclude that the extended Nikiforov-Uvarov method has limited, if any, value when considering similar problems in quantum mechanics.","weakest_assumption":"That the radial equation from the non-relativistic Dirac limit reduces to a Heun equation to which the extended Nikiforov-Uvarov method can be applied to produce a meaningful quantization condition whose polynomial-solution requirements are checkable, even though the paper ultimately shows those requirements are not satisfied."}},"verdict_id":"11c8855a-d275-48d1-a537-96e8d5f2e893"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:be227f2d908eef10c37cc51100c06b2e54054a3b9944d2380b3aac032862c112","target":"record","created_at":"2026-05-21T01:04:26Z","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":"edf506c7bbe78362f68016372d3d66fc531beefce6af01a7c298ef620b069c64","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-04-30T07:24:56Z","title_canon_sha256":"9b8134ddf2527ce4f92643db382aa17fe6cf192217a44c9947eef06bbeca44ec"},"schema_version":"1.0","source":{"id":"2604.27522","kind":"arxiv","version":1}},"canonical_sha256":"570130b994d5c859170b83ab93a74e0748ff593cbaeb7cddf594e9f92a1eec77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"570130b994d5c859170b83ab93a74e0748ff593cbaeb7cddf594e9f92a1eec77","first_computed_at":"2026-05-21T01:04:26.606382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:26.606382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fu3DT2cuUCpl5uitMIneFkvVHhWY3qGFtHSuoBL/218VtIYcNYrbxoednCWotaH0UtGxy+xWU9KKL94BJ6MTAg==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:26.607061Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.27522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8be267ea8ea7d6547600c629b6cc2a905ac0be5357a8449f995b281846b9026e","sha256:be227f2d908eef10c37cc51100c06b2e54054a3b9944d2380b3aac032862c112","sha256:4f0a0726ddb2f5f5cd5689c5ac108277c876657d70d4ac6d55a46a63802b7844"],"state_sha256":"c8fdcfbf92a3a20b2a803e4070606ed8c228a493807919bb4355fe34647e931f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5lI+xXOY3cOV1OIqx6fUUPeuSDVlIjZgPpRbRcECHruVdNhmZJk+HtyU7x+x+YuJqTF9oq5c0bv/4TzPVcU5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:52:05.497241Z","bundle_sha256":"858e4381c44830356d2acde0f1096e568126b6fa7ff708fa0816963182d87c42"}}