{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:V7J57EOOK3A3P5RAB55IIAW5G3","short_pith_number":"pith:V7J57EOO","canonical_record":{"source":{"id":"1609.00315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-31T10:30:15Z","cross_cats_sorted":[],"title_canon_sha256":"4c29b977fba51029b12522b782275bb44389da23611706445e14ca1b1e72c9d5","abstract_canon_sha256":"a17f5616f43782c9dba964f9061bd9753dc194ed9669f4baa9d7e2d7aa023a87"},"schema_version":"1.0"},"canonical_sha256":"afd3df91ce56c1b7f6200f7a8402dd36d7e66fde04a2dde02f4d60f89291ecbc","source":{"kind":"arxiv","id":"1609.00315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00315","created_at":"2026-05-18T01:06:25Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00315v1","created_at":"2026-05-18T01:06:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00315","created_at":"2026-05-18T01:06:25Z"},{"alias_kind":"pith_short_12","alias_value":"V7J57EOOK3A3","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"V7J57EOOK3A3P5RA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"V7J57EOO","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:V7J57EOOK3A3P5RAB55IIAW5G3","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-31T10:30:15Z","cross_cats_sorted":[],"title_canon_sha256":"4c29b977fba51029b12522b782275bb44389da23611706445e14ca1b1e72c9d5","abstract_canon_sha256":"a17f5616f43782c9dba964f9061bd9753dc194ed9669f4baa9d7e2d7aa023a87"},"schema_version":"1.0"},"canonical_sha256":"afd3df91ce56c1b7f6200f7a8402dd36d7e66fde04a2dde02f4d60f89291ecbc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:25.155567Z","signature_b64":"tl3xJm/j9ocEjGlPGQAA54RmrdUchUFRLTeupUEn+o7lKfOIDzn8n4l77og8FaVw5VmLAsbdfNLoHE8IE4MsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afd3df91ce56c1b7f6200f7a8402dd36d7e66fde04a2dde02f4d60f89291ecbc","last_reissued_at":"2026-05-18T01:06:25.155167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:25.155167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00315","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":"2026-05-18T01:06:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xFCrmiYi7FiAPuU5DN96pDtSCvb5pG0ipqpUntsp1aR0fgJ4uGt3Cu3NqQCxu/3UpTWmZnCEGPD5te17A614Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:53:53.071719Z"},"content_sha256":"efa5dafadd49a02f26bbc0a16cd61e319ed4507bc48a6213f560bfdac8ed858f","schema_version":"1.0","event_id":"sha256:efa5dafadd49a02f26bbc0a16cd61e319ed4507bc48a6213f560bfdac8ed858f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:V7J57EOOK3A3P5RAB55IIAW5G3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relativistic Killingbeck Energy States Under an External Magnetic Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Husein Mehraban, Mahdi Eshghi, Sameer M. Ikhdair","submitted_at":"2016-08-31T10:30:15Z","abstract_excerpt":"We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00315","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":"2026-05-18T01:06:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OUn+ZRG7iy/pauZMfZ4TDCTkjkOkCn2/JVqJBSNQ7VBZ1ulIainefQial7wIVhEOTZ9okfyqXg8TUKfyk15tCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:53:53.072056Z"},"content_sha256":"5db44b4ba19dbabbe6c5dc49cb2533a2af701e810beb500e3811bc67abad3be4","schema_version":"1.0","event_id":"sha256:5db44b4ba19dbabbe6c5dc49cb2533a2af701e810beb500e3811bc67abad3be4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7J57EOOK3A3P5RAB55IIAW5G3/bundle.json","state_url":"https://pith.science/pith/V7J57EOOK3A3P5RAB55IIAW5G3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7J57EOOK3A3P5RAB55IIAW5G3/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":"2026-05-30T08:53:53Z","links":{"resolver":"https://pith.science/pith/V7J57EOOK3A3P5RAB55IIAW5G3","bundle":"https://pith.science/pith/V7J57EOOK3A3P5RAB55IIAW5G3/bundle.json","state":"https://pith.science/pith/V7J57EOOK3A3P5RAB55IIAW5G3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7J57EOOK3A3P5RAB55IIAW5G3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:V7J57EOOK3A3P5RAB55IIAW5G3","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":"a17f5616f43782c9dba964f9061bd9753dc194ed9669f4baa9d7e2d7aa023a87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-31T10:30:15Z","title_canon_sha256":"4c29b977fba51029b12522b782275bb44389da23611706445e14ca1b1e72c9d5"},"schema_version":"1.0","source":{"id":"1609.00315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00315","created_at":"2026-05-18T01:06:25Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00315v1","created_at":"2026-05-18T01:06:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00315","created_at":"2026-05-18T01:06:25Z"},{"alias_kind":"pith_short_12","alias_value":"V7J57EOOK3A3","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"V7J57EOOK3A3P5RA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"V7J57EOO","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:5db44b4ba19dbabbe6c5dc49cb2533a2af701e810beb500e3811bc67abad3be4","target":"graph","created_at":"2026-05-18T01:06:25Z","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":"We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries,","authors_text":"Husein Mehraban, Mahdi Eshghi, Sameer M. Ikhdair","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-31T10:30:15Z","title":"Relativistic Killingbeck Energy States Under an External Magnetic Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00315","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:efa5dafadd49a02f26bbc0a16cd61e319ed4507bc48a6213f560bfdac8ed858f","target":"record","created_at":"2026-05-18T01:06:25Z","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":"a17f5616f43782c9dba964f9061bd9753dc194ed9669f4baa9d7e2d7aa023a87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-31T10:30:15Z","title_canon_sha256":"4c29b977fba51029b12522b782275bb44389da23611706445e14ca1b1e72c9d5"},"schema_version":"1.0","source":{"id":"1609.00315","kind":"arxiv","version":1}},"canonical_sha256":"afd3df91ce56c1b7f6200f7a8402dd36d7e66fde04a2dde02f4d60f89291ecbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afd3df91ce56c1b7f6200f7a8402dd36d7e66fde04a2dde02f4d60f89291ecbc","first_computed_at":"2026-05-18T01:06:25.155167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:25.155167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tl3xJm/j9ocEjGlPGQAA54RmrdUchUFRLTeupUEn+o7lKfOIDzn8n4l77og8FaVw5VmLAsbdfNLoHE8IE4MsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:25.155567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efa5dafadd49a02f26bbc0a16cd61e319ed4507bc48a6213f560bfdac8ed858f","sha256:5db44b4ba19dbabbe6c5dc49cb2533a2af701e810beb500e3811bc67abad3be4"],"state_sha256":"0eee51fae25e8c4a40079b0aecca1ac21c8b5b9cd86ccd32e8c7a10bd881d1b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9uKa1ZBrVU0+cwLXwqtwYSfL4NlOW7Yah32sVuG3UobrmCynboZYwaNZ4dlO2TzlyggCeMJ9f6Vmf2NeReVNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:53:53.073933Z","bundle_sha256":"81fc4cac5343dede5e8da6fc22513608c7e5ba0bbd97b63ea370d420c203d190"}}