{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DQKOAIALJOQKHVSOE3UUH3NKP2","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":"a31049faf4be34415ce22e58cf9e99a175d3f748d3e83e92440ede032968f182","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-21T13:29:32Z","title_canon_sha256":"48cfaa9f58f46630136f9b2fab2bcc573c48c316309ce0f4f4f04688e6dbc742"},"schema_version":"1.0","source":{"id":"1207.5135","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5135","created_at":"2026-05-18T02:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5135v2","created_at":"2026-05-18T02:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5135","created_at":"2026-05-18T02:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"DQKOAIALJOQK","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DQKOAIALJOQKHVSO","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DQKOAIAL","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:6cf1e9207ac4e34a291d5784e406017b5363946920372196d3e8e93cf0c40c32","target":"graph","created_at":"2026-05-18T02:58:43Z","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"},"paper":{"abstract_excerpt":"Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the $\\ell$-wave solutions of the Schr\\\"{o}dinger equation with the Manning-Rosen potential. The equation of energy eigenvalues equation and the corresponding wavefunctions have been obtained explicitly. Three different Pekeris-type approximation schemes have been used to deal with the centrifugal term. To show the accuracy of our results, we have calculated the eigenvalues numerically for arbitrary quantum numbers $n$ and $\\ell$ for some diatomic molecules (HCl, CH, LiH and CO). It is found that the resu","authors_text":"B.J. Falaye, C. A. Onate, K. J. Oyewumi, M. A. Punyasena, T. T. Ibrahim","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-21T13:29:32Z","title":"Bound state solutions of the Manning-Rosen potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5135","kind":"arxiv","version":2},"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":"sha256:978d0800a374ab2d16145ba35de0e6a62ca500e210e74712d8e574f19d80c483","target":"record","created_at":"2026-05-18T02:58:43Z","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":"a31049faf4be34415ce22e58cf9e99a175d3f748d3e83e92440ede032968f182","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-21T13:29:32Z","title_canon_sha256":"48cfaa9f58f46630136f9b2fab2bcc573c48c316309ce0f4f4f04688e6dbc742"},"schema_version":"1.0","source":{"id":"1207.5135","kind":"arxiv","version":2}},"canonical_sha256":"1c14e0200b4ba0a3d64e26e943edaa7eaba4c7b4f6ebdc61290e0322854fc0ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c14e0200b4ba0a3d64e26e943edaa7eaba4c7b4f6ebdc61290e0322854fc0ca","first_computed_at":"2026-05-18T02:58:43.539650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:43.539650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BIL4jFjQi68wxrsYW3DGPLYzS6MCNASDGGNF4ZJjh9gE32NNlm83vsxo1lfxNl8V3ThoJL4CX0z0SRMwhuwzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:43.540226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5135","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:978d0800a374ab2d16145ba35de0e6a62ca500e210e74712d8e574f19d80c483","sha256:6cf1e9207ac4e34a291d5784e406017b5363946920372196d3e8e93cf0c40c32"],"state_sha256":"fa1c4155cd63363aa5578413042e8b5c4248e9d824a9a0aa53b9ecada91dc6cd"}