{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QQAT7OWI3AUYPZDDKISKBDF4KW","short_pith_number":"pith:QQAT7OWI","canonical_record":{"source":{"id":"1204.1426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-06T07:57:40Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"82cc161de60436b7980e50ea283fbb67960f5f5e26f3d73d78c250c7b7ce3734","abstract_canon_sha256":"7723c17ac52d36527bd719e093b4953474d4dbeaff4df4665944ba82fb272845"},"schema_version":"1.0"},"canonical_sha256":"84013fbac8d82987e4635224a08cbc55beae8259daaf6d784d8debae5d981f97","source":{"kind":"arxiv","id":"1204.1426","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1426","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1426v1","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1426","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"pith_short_12","alias_value":"QQAT7OWI3AUY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QQAT7OWI3AUYPZDD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QQAT7OWI","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QQAT7OWI3AUYPZDDKISKBDF4KW","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-06T07:57:40Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"82cc161de60436b7980e50ea283fbb67960f5f5e26f3d73d78c250c7b7ce3734","abstract_canon_sha256":"7723c17ac52d36527bd719e093b4953474d4dbeaff4df4665944ba82fb272845"},"schema_version":"1.0"},"canonical_sha256":"84013fbac8d82987e4635224a08cbc55beae8259daaf6d784d8debae5d981f97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:35.230613Z","signature_b64":"lp/LTQn+xBF974DYxAWtEQf4/p6fsXVeemdFLHk4MU63HzZtBa706Ejd/JT0fqfcTMw9Guoj6kc8atA1ShmXDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84013fbac8d82987e4635224a08cbc55beae8259daaf6d784d8debae5d981f97","last_reissued_at":"2026-05-18T03:51:35.229861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:35.229861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1426","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g6dAKWmrx1PmElXgn2y9A0mv4bvDX/vxqADSqFEZbgfCboC6VTE+aN4/UKQD8RwV7VlCOR0RyBcRKGJKpSfkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:37:33.235301Z"},"content_sha256":"376b2477d585a0005541616b1b3783428a972f8c1d010fa4259b9ef35a09e63c","schema_version":"1.0","event_id":"sha256:376b2477d585a0005541616b1b3783428a972f8c1d010fa4259b9ef35a09e63c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QQAT7OWI3AUYPZDDKISKBDF4KW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Analytical Solutions of a Two-Term Diatomic Molecular Potential with Centrifugal Barrier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Altug Arda, Ramazan Sever","submitted_at":"2012-04-06T07:57:40Z","abstract_excerpt":"Approximate analytical bound state solutions of the radial Schr\\\"odinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\\geq1$ and $q=0$. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulth\\'{e}n potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1426","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AseLOU8qYStD8KXHv8iWeEx2DPxBaOZ42jxafhAzksEqB0uUFAxhpwZwigB/RwftuJSwGctZl27L4x13+H35Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:37:33.235894Z"},"content_sha256":"7e22c7cabad02c10b0e4fc4fa7e8d87a147e63c55b14283f219835c4ec560da7","schema_version":"1.0","event_id":"sha256:7e22c7cabad02c10b0e4fc4fa7e8d87a147e63c55b14283f219835c4ec560da7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQAT7OWI3AUYPZDDKISKBDF4KW/bundle.json","state_url":"https://pith.science/pith/QQAT7OWI3AUYPZDDKISKBDF4KW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQAT7OWI3AUYPZDDKISKBDF4KW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T01:37:33Z","links":{"resolver":"https://pith.science/pith/QQAT7OWI3AUYPZDDKISKBDF4KW","bundle":"https://pith.science/pith/QQAT7OWI3AUYPZDDKISKBDF4KW/bundle.json","state":"https://pith.science/pith/QQAT7OWI3AUYPZDDKISKBDF4KW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQAT7OWI3AUYPZDDKISKBDF4KW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QQAT7OWI3AUYPZDDKISKBDF4KW","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":"7723c17ac52d36527bd719e093b4953474d4dbeaff4df4665944ba82fb272845","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-06T07:57:40Z","title_canon_sha256":"82cc161de60436b7980e50ea283fbb67960f5f5e26f3d73d78c250c7b7ce3734"},"schema_version":"1.0","source":{"id":"1204.1426","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1426","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1426v1","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1426","created_at":"2026-05-18T03:51:35Z"},{"alias_kind":"pith_short_12","alias_value":"QQAT7OWI3AUY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QQAT7OWI3AUYPZDD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QQAT7OWI","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:7e22c7cabad02c10b0e4fc4fa7e8d87a147e63c55b14283f219835c4ec560da7","target":"graph","created_at":"2026-05-18T03:51:35Z","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":"Approximate analytical bound state solutions of the radial Schr\\\"odinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\\geq1$ and $q=0$. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulth\\'{e}n potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.","authors_text":"Altug Arda, Ramazan Sever","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-06T07:57:40Z","title":"Approximate Analytical Solutions of a Two-Term Diatomic Molecular Potential with Centrifugal Barrier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1426","kind":"arxiv","version":1},"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":"sha256:376b2477d585a0005541616b1b3783428a972f8c1d010fa4259b9ef35a09e63c","target":"record","created_at":"2026-05-18T03:51:35Z","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":"7723c17ac52d36527bd719e093b4953474d4dbeaff4df4665944ba82fb272845","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-06T07:57:40Z","title_canon_sha256":"82cc161de60436b7980e50ea283fbb67960f5f5e26f3d73d78c250c7b7ce3734"},"schema_version":"1.0","source":{"id":"1204.1426","kind":"arxiv","version":1}},"canonical_sha256":"84013fbac8d82987e4635224a08cbc55beae8259daaf6d784d8debae5d981f97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84013fbac8d82987e4635224a08cbc55beae8259daaf6d784d8debae5d981f97","first_computed_at":"2026-05-18T03:51:35.229861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:35.229861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lp/LTQn+xBF974DYxAWtEQf4/p6fsXVeemdFLHk4MU63HzZtBa706Ejd/JT0fqfcTMw9Guoj6kc8atA1ShmXDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:35.230613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1426","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:376b2477d585a0005541616b1b3783428a972f8c1d010fa4259b9ef35a09e63c","sha256:7e22c7cabad02c10b0e4fc4fa7e8d87a147e63c55b14283f219835c4ec560da7"],"state_sha256":"1bb4a1acc3bdd73b7b11105eb6e5cd55fa2734e67cb77f68f2ed0a4d72073d83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJVqAehsxOgG1Ld7UDA2DyPFAsVold2C0HqOTSsI/jZhoo8ydqn+sq9g5vXee0dDoCIYuNvq8WMmfPAb7Y9oDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:37:33.239071Z","bundle_sha256":"5a78a9449734f334ff0133a623ffb485f674f461e38d6d9d1c6f534c9615b2cf"}}