{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:A3O5SWKHKMANCUQNCVCQQ5M6GU","short_pith_number":"pith:A3O5SWKH","schema_version":"1.0","canonical_sha256":"06ddd959475300d1520d154508759e352d1dcc32a10b197773ff277c2f515968","source":{"kind":"arxiv","id":"hep-th/0210149","version":1},"attestation_state":"computed","paper":{"title":"Discrete Spectra of Semirelativistic Hamiltonians","license":"","headline":"","cross_cats":["hep-ph","math-ph","math.MP","nucl-th"],"primary_cat":"hep-th","authors_text":"F. F. Schoeberl, Richard Hall, Wolfgang Lucha","submitted_at":"2002-10-16T09:08:54Z","abstract_excerpt":"We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \\beta \\sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation. Every Hamiltonian in this class of operators consists of the relativistic kinetic energy \\beta \\sqrt{m^2 + p^2} (where \\beta > 0 allows for the possibility of more than one particles of mass m) and a spherically symmetric attractive potential V(r), r = |x|. In general, accurate eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of a "},"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":"hep-th/0210149","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2002-10-16T09:08:54Z","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"title_canon_sha256":"ffa17dddf6313f7ef0ab441dc84a64b1d119acd2e37de0ef2697094d896653b2","abstract_canon_sha256":"c7bbb896f0cacc40e0af64e526c5c8d1f4c45a97b6e5dd33f0039cc1ad715e85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:53.621272Z","signature_b64":"o9ZVHZgcAStlZgv9EE2/Tck/nkx+HIBBtq9/fcKzCMzNujHW/VHOVVe9dFzMmSneEJtwMZ0czs2IviwsE/kUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06ddd959475300d1520d154508759e352d1dcc32a10b197773ff277c2f515968","last_reissued_at":"2026-05-18T02:35:53.620775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:53.620775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete Spectra of Semirelativistic Hamiltonians","license":"","headline":"","cross_cats":["hep-ph","math-ph","math.MP","nucl-th"],"primary_cat":"hep-th","authors_text":"F. F. Schoeberl, Richard Hall, Wolfgang Lucha","submitted_at":"2002-10-16T09:08:54Z","abstract_excerpt":"We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \\beta \\sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation. Every Hamiltonian in this class of operators consists of the relativistic kinetic energy \\beta \\sqrt{m^2 + p^2} (where \\beta > 0 allows for the possibility of more than one particles of mass m) and a spherically symmetric attractive potential V(r), r = |x|. In general, accurate eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0210149","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":"hep-th/0210149","created_at":"2026-05-18T02:35:53.620853+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0210149v1","created_at":"2026-05-18T02:35:53.620853+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0210149","created_at":"2026-05-18T02:35:53.620853+00:00"},{"alias_kind":"pith_short_12","alias_value":"A3O5SWKHKMAN","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"A3O5SWKHKMANCUQN","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"A3O5SWKH","created_at":"2026-05-18T12:25:50.845339+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/A3O5SWKHKMANCUQNCVCQQ5M6GU","json":"https://pith.science/pith/A3O5SWKHKMANCUQNCVCQQ5M6GU.json","graph_json":"https://pith.science/api/pith-number/A3O5SWKHKMANCUQNCVCQQ5M6GU/graph.json","events_json":"https://pith.science/api/pith-number/A3O5SWKHKMANCUQNCVCQQ5M6GU/events.json","paper":"https://pith.science/paper/A3O5SWKH"},"agent_actions":{"view_html":"https://pith.science/pith/A3O5SWKHKMANCUQNCVCQQ5M6GU","download_json":"https://pith.science/pith/A3O5SWKHKMANCUQNCVCQQ5M6GU.json","view_paper":"https://pith.science/paper/A3O5SWKH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0210149&json=true","fetch_graph":"https://pith.science/api/pith-number/A3O5SWKHKMANCUQNCVCQQ5M6GU/graph.json","fetch_events":"https://pith.science/api/pith-number/A3O5SWKHKMANCUQNCVCQQ5M6GU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A3O5SWKHKMANCUQNCVCQQ5M6GU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A3O5SWKHKMANCUQNCVCQQ5M6GU/action/storage_attestation","attest_author":"https://pith.science/pith/A3O5SWKHKMANCUQNCVCQQ5M6GU/action/author_attestation","sign_citation":"https://pith.science/pith/A3O5SWKHKMANCUQNCVCQQ5M6GU/action/citation_signature","submit_replication":"https://pith.science/pith/A3O5SWKHKMANCUQNCVCQQ5M6GU/action/replication_record"}},"created_at":"2026-05-18T02:35:53.620853+00:00","updated_at":"2026-05-18T02:35:53.620853+00:00"}