{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VJV37ESKP7CJEVU2JVCRA2JXBK","short_pith_number":"pith:VJV37ESK","canonical_record":{"source":{"id":"1004.3905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:43:56Z","cross_cats_sorted":["math.MP","physics.atm-clus","quant-ph"],"title_canon_sha256":"83181196faba396cc661747a714913aba236edef2904ad810599bdeca2bf2702","abstract_canon_sha256":"a457294b7bc0693017fdc8cc0249744a8075babc1be73a08dea53db97665b7bc"},"schema_version":"1.0"},"canonical_sha256":"aa6bbf924a7fc492569a4d451069370a9c6b8192ce855bb091f7c6437bd7c9fb","source":{"kind":"arxiv","id":"1004.3905","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3905","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3905v1","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3905","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"VJV37ESKP7CJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VJV37ESKP7CJEVU2","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VJV37ESK","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VJV37ESKP7CJEVU2JVCRA2JXBK","target":"record","payload":{"canonical_record":{"source":{"id":"1004.3905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:43:56Z","cross_cats_sorted":["math.MP","physics.atm-clus","quant-ph"],"title_canon_sha256":"83181196faba396cc661747a714913aba236edef2904ad810599bdeca2bf2702","abstract_canon_sha256":"a457294b7bc0693017fdc8cc0249744a8075babc1be73a08dea53db97665b7bc"},"schema_version":"1.0"},"canonical_sha256":"aa6bbf924a7fc492569a4d451069370a9c6b8192ce855bb091f7c6437bd7c9fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:55.138942Z","signature_b64":"i8PXu9uw0UVAR2/DhbyEK5qCThZf9NGxjCnS0XAiNcBXH8WLlR9Dz1///Lr7dKPC1PMRfIFf20RpPJBnR8VaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa6bbf924a7fc492569a4d451069370a9c6b8192ce855bb091f7c6437bd7c9fb","last_reissued_at":"2026-05-18T02:07:55.138188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:55.138188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.3905","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":"2026-05-18T02:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSg6Y02zh+xvAsBsp6T5VPvDeUQwhiq29xoikrtErc6TtRG9QY7Geu+KdDNff1oOp67gvmk2qaoHJ4o9TbboAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:30:08.053227Z"},"content_sha256":"112af9bdc9e8694b8abcd4339421ab7585d3905f7f90d863fba9935a6f1b49a4","schema_version":"1.0","event_id":"sha256:112af9bdc9e8694b8abcd4339421ab7585d3905f7f90d863fba9935a6f1b49a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VJV37ESKP7CJEVU2JVCRA2JXBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extending the class of solvable potentials: II. Screened Coulomb potential with a barrier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.atm-clus","quant-ph"],"primary_cat":"math-ph","authors_text":"A. D. Alhaidari","submitted_at":"2010-04-22T12:43:56Z","abstract_excerpt":"This is the second article in a series where we succeed in enlarging the class of solvable problems in one and three dimensions. We do that by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. Consequently, the wave equation becomes equivalent to a three-term recursion relation for the expansion coefficients of the wavefunction in the basis. Finding solutions of the recursion relation is equivalent to solving the original problem. This method gives a larger class of solvable potentials. The usual diagonal representation constra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3905","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":"2026-05-18T02:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icJhisKSb482yZbKGwTo+Y/uyEbaHuc9la7te3spF0vBku56ubJ46MT6kd8TCP7ZBVhM3K13cRoiCnOd7qWEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:30:08.053633Z"},"content_sha256":"fb3285be0b8d67e3a2d1346579a24eca59a8ff58d549863e0484b74e255c4da9","schema_version":"1.0","event_id":"sha256:fb3285be0b8d67e3a2d1346579a24eca59a8ff58d549863e0484b74e255c4da9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VJV37ESKP7CJEVU2JVCRA2JXBK/bundle.json","state_url":"https://pith.science/pith/VJV37ESKP7CJEVU2JVCRA2JXBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VJV37ESKP7CJEVU2JVCRA2JXBK/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":"2026-06-07T15:30:08Z","links":{"resolver":"https://pith.science/pith/VJV37ESKP7CJEVU2JVCRA2JXBK","bundle":"https://pith.science/pith/VJV37ESKP7CJEVU2JVCRA2JXBK/bundle.json","state":"https://pith.science/pith/VJV37ESKP7CJEVU2JVCRA2JXBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VJV37ESKP7CJEVU2JVCRA2JXBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VJV37ESKP7CJEVU2JVCRA2JXBK","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":"a457294b7bc0693017fdc8cc0249744a8075babc1be73a08dea53db97665b7bc","cross_cats_sorted":["math.MP","physics.atm-clus","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:43:56Z","title_canon_sha256":"83181196faba396cc661747a714913aba236edef2904ad810599bdeca2bf2702"},"schema_version":"1.0","source":{"id":"1004.3905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3905","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3905v1","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3905","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"VJV37ESKP7CJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VJV37ESKP7CJEVU2","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VJV37ESK","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:fb3285be0b8d67e3a2d1346579a24eca59a8ff58d549863e0484b74e255c4da9","target":"graph","created_at":"2026-05-18T02:07:55Z","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":"This is the second article in a series where we succeed in enlarging the class of solvable problems in one and three dimensions. We do that by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator. Consequently, the wave equation becomes equivalent to a three-term recursion relation for the expansion coefficients of the wavefunction in the basis. Finding solutions of the recursion relation is equivalent to solving the original problem. This method gives a larger class of solvable potentials. The usual diagonal representation constra","authors_text":"A. D. Alhaidari","cross_cats":["math.MP","physics.atm-clus","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:43:56Z","title":"Extending the class of solvable potentials: II. Screened Coulomb potential with a barrier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3905","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":"sha256:112af9bdc9e8694b8abcd4339421ab7585d3905f7f90d863fba9935a6f1b49a4","target":"record","created_at":"2026-05-18T02:07:55Z","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":"a457294b7bc0693017fdc8cc0249744a8075babc1be73a08dea53db97665b7bc","cross_cats_sorted":["math.MP","physics.atm-clus","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:43:56Z","title_canon_sha256":"83181196faba396cc661747a714913aba236edef2904ad810599bdeca2bf2702"},"schema_version":"1.0","source":{"id":"1004.3905","kind":"arxiv","version":1}},"canonical_sha256":"aa6bbf924a7fc492569a4d451069370a9c6b8192ce855bb091f7c6437bd7c9fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa6bbf924a7fc492569a4d451069370a9c6b8192ce855bb091f7c6437bd7c9fb","first_computed_at":"2026-05-18T02:07:55.138188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:55.138188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i8PXu9uw0UVAR2/DhbyEK5qCThZf9NGxjCnS0XAiNcBXH8WLlR9Dz1///Lr7dKPC1PMRfIFf20RpPJBnR8VaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:55.138942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:112af9bdc9e8694b8abcd4339421ab7585d3905f7f90d863fba9935a6f1b49a4","sha256:fb3285be0b8d67e3a2d1346579a24eca59a8ff58d549863e0484b74e255c4da9"],"state_sha256":"d5df2f804f91d68397ddb6d2d726086de107362a0323e88ffed7a4b13280d92e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sEMk4KleioXmQVTEyWP4HgmkFZajPha26AMfA0fiD02SL27IFmZa3VcEza8LHx0VaSKUSC08e29GcetfvGqeCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T15:30:08.056288Z","bundle_sha256":"5ca7b4d529806a6b7f9513364835f40a28366f154b81bf35fa15f28c94b0a990"}}