{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:QTSHIZQQP7RNUJLAPTX7PZNTEF","short_pith_number":"pith:QTSHIZQQ","schema_version":"1.0","canonical_sha256":"84e47466107fe2da25607ceff7e5b3214d63a78cc2494555d2e5fd7a6b87beff","source":{"kind":"arxiv","id":"math-ph/9908020","version":2},"attestation_state":"computed","paper":{"title":"Self-energy of electrons in non-perturbative QED","license":"","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Elliott Lieb, Michael Loss","submitted_at":"1999-08-20T21:06:40Z","abstract_excerpt":"Various models of charged particles interacting with a quantized, ultraviolet cutoff radiation field (but not with each other) are investigated. Upper and lower bounds are found for the self- or ground state-energies without mass renormalization. For $N$ fermions the bounds are proportional to $N$, but for bosons they are sublinear, which implies `binding', and hence that `free' bosons are never free. Both `relativistic' and non-relativistic kinematics are considered. Our bounds are non-perturbative and differ significantly from the predictions of perturbation theory."},"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":"math-ph/9908020","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1999-08-20T21:06:40Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"12badfe77abdcfd99d392f6d1859a7f86c6b31fb686c61f25809674e0fcd238f","abstract_canon_sha256":"e02f15f5b1985eea97e3220e8b92eda657b6084632ca248d6bf7bddefd9b1212"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:11.080105Z","signature_b64":"GXvUsBop4PFmoSbUzSo1IRdG8JbcP0nQ6nw2r+LhWLRpnjxMLurJqpYSZviL/7JvKWZ727kefowJvamDXdPQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84e47466107fe2da25607ceff7e5b3214d63a78cc2494555d2e5fd7a6b87beff","last_reissued_at":"2026-07-04T14:34:11.079751Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:11.079751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-energy of electrons in non-perturbative QED","license":"","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Elliott Lieb, Michael Loss","submitted_at":"1999-08-20T21:06:40Z","abstract_excerpt":"Various models of charged particles interacting with a quantized, ultraviolet cutoff radiation field (but not with each other) are investigated. Upper and lower bounds are found for the self- or ground state-energies without mass renormalization. For $N$ fermions the bounds are proportional to $N$, but for bosons they are sublinear, which implies `binding', and hence that `free' bosons are never free. Both `relativistic' and non-relativistic kinematics are considered. Our bounds are non-perturbative and differ significantly from the predictions of perturbation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9908020","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/9908020/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math-ph/9908020","created_at":"2026-07-04T14:34:11.079806+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9908020v2","created_at":"2026-07-04T14:34:11.079806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9908020","created_at":"2026-07-04T14:34:11.079806+00:00"},{"alias_kind":"pith_short_12","alias_value":"QTSHIZQQP7RN","created_at":"2026-07-04T14:34:11.079806+00:00"},{"alias_kind":"pith_short_16","alias_value":"QTSHIZQQP7RNUJLA","created_at":"2026-07-04T14:34:11.079806+00:00"},{"alias_kind":"pith_short_8","alias_value":"QTSHIZQQ","created_at":"2026-07-04T14:34:11.079806+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.04876","citing_title":"Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions","ref_index":38,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF","json":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF.json","graph_json":"https://pith.science/api/pith-number/QTSHIZQQP7RNUJLAPTX7PZNTEF/graph.json","events_json":"https://pith.science/api/pith-number/QTSHIZQQP7RNUJLAPTX7PZNTEF/events.json","paper":"https://pith.science/paper/QTSHIZQQ"},"agent_actions":{"view_html":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF","download_json":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF.json","view_paper":"https://pith.science/paper/QTSHIZQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/9908020&json=true","fetch_graph":"https://pith.science/api/pith-number/QTSHIZQQP7RNUJLAPTX7PZNTEF/graph.json","fetch_events":"https://pith.science/api/pith-number/QTSHIZQQP7RNUJLAPTX7PZNTEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF/action/storage_attestation","attest_author":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF/action/author_attestation","sign_citation":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF/action/citation_signature","submit_replication":"https://pith.science/pith/QTSHIZQQP7RNUJLAPTX7PZNTEF/action/replication_record"}},"created_at":"2026-07-04T14:34:11.079806+00:00","updated_at":"2026-07-04T14:34:11.079806+00:00"}