{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:SS2ZKILKG4YQHLHNACY6YFDC2T","short_pith_number":"pith:SS2ZKILK","schema_version":"1.0","canonical_sha256":"94b595216a373103aced00b1ec1462d4dd0dc3a36cdd8c677cf839ea672c30b2","source":{"kind":"arxiv","id":"1202.1814","version":1},"attestation_state":"computed","paper":{"title":"Dirac eigenvalues for a softcore Coulomb potential in d dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.atom-ph"],"primary_cat":"math-ph","authors_text":"Petr Zorin, Richard L. Hall","submitted_at":"2012-02-08T20:51:17Z","abstract_excerpt":"A single fermion is bound by a softcore central Coulomb potential V(r) = -v/(r^q + b^q)^(1/q), v>0, b>0, q \\ge 1, in d>1 spatial dimensions. Envelope theory is used to construct analytic lower bounds for the discrete Dirac energy spectrum. The results are compared to accurate eigenvalues obtained numerically."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1202.1814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-08T20:51:17Z","cross_cats_sorted":["math.MP","physics.atom-ph"],"title_canon_sha256":"1c01df8df4e9140cffda80993368b40c39c1be23fe9dbae4c0bb7ed0e303fbb5","abstract_canon_sha256":"87ad60ef72e84b5d964359feef416e621da0d53618af1310e5de52d9937bbc86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:32.110568Z","signature_b64":"QVsfasTn8RCooFVqVnyES8dxLrtNY/oYDUVHZCJwiBvEkkUaS2mVf4U9Ic+ypIzUpRbbdhuUl1JqLHm80xoODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94b595216a373103aced00b1ec1462d4dd0dc3a36cdd8c677cf839ea672c30b2","last_reissued_at":"2026-05-18T01:58:32.110025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:32.110025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirac eigenvalues for a softcore Coulomb potential in d dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.atom-ph"],"primary_cat":"math-ph","authors_text":"Petr Zorin, Richard L. Hall","submitted_at":"2012-02-08T20:51:17Z","abstract_excerpt":"A single fermion is bound by a softcore central Coulomb potential V(r) = -v/(r^q + b^q)^(1/q), v>0, b>0, q \\ge 1, in d>1 spatial dimensions. Envelope theory is used to construct analytic lower bounds for the discrete Dirac energy spectrum. The results are compared to accurate eigenvalues obtained numerically."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1814","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.1814","created_at":"2026-05-18T01:58:32.110122+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.1814v1","created_at":"2026-05-18T01:58:32.110122+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.1814","created_at":"2026-05-18T01:58:32.110122+00:00"},{"alias_kind":"pith_short_12","alias_value":"SS2ZKILKG4YQ","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"SS2ZKILKG4YQHLHN","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"SS2ZKILK","created_at":"2026-05-18T12:27:20.899486+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T","json":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T.json","graph_json":"https://pith.science/api/pith-number/SS2ZKILKG4YQHLHNACY6YFDC2T/graph.json","events_json":"https://pith.science/api/pith-number/SS2ZKILKG4YQHLHNACY6YFDC2T/events.json","paper":"https://pith.science/paper/SS2ZKILK"},"agent_actions":{"view_html":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T","download_json":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T.json","view_paper":"https://pith.science/paper/SS2ZKILK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.1814&json=true","fetch_graph":"https://pith.science/api/pith-number/SS2ZKILKG4YQHLHNACY6YFDC2T/graph.json","fetch_events":"https://pith.science/api/pith-number/SS2ZKILKG4YQHLHNACY6YFDC2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T/action/storage_attestation","attest_author":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T/action/author_attestation","sign_citation":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T/action/citation_signature","submit_replication":"https://pith.science/pith/SS2ZKILKG4YQHLHNACY6YFDC2T/action/replication_record"}},"created_at":"2026-05-18T01:58:32.110122+00:00","updated_at":"2026-05-18T01:58:32.110122+00:00"}