{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5RVWE53JAUP6KKRGFAWQ42IA44","short_pith_number":"pith:5RVWE53J","schema_version":"1.0","canonical_sha256":"ec6b627769051fe52a26282d0e6900e7259748e892c96ff47a2be4ea853bb898","source":{"kind":"arxiv","id":"1705.08554","version":1},"attestation_state":"computed","paper":{"title":"On beam models and their paraxial approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","physics.class-ph"],"primary_cat":"physics.optics","authors_text":"B. King, W. J. Waters","submitted_at":"2017-05-23T22:42:25Z","abstract_excerpt":"We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak l"},"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":"1705.08554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2017-05-23T22:42:25Z","cross_cats_sorted":["hep-ph","physics.class-ph"],"title_canon_sha256":"79440290d51e12dbbbac059b17d4dda8e98cc29875639c2df90abda774e86a9a","abstract_canon_sha256":"d3bc2afa0e7789eefea438d5b814d3fa6a54f7c7d1043e0598791e26ea7939c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:57.647194Z","signature_b64":"3oDAcDVsBeiaFN9oRGQRPDdHcO/B4jr8EQYK8ImB5wGax6t1t5lFQYB+CxOEqC3k6Hljpui86zmk4Uk5+ZTxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec6b627769051fe52a26282d0e6900e7259748e892c96ff47a2be4ea853bb898","last_reissued_at":"2026-05-18T00:25:57.646552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:57.646552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On beam models and their paraxial approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","physics.class-ph"],"primary_cat":"physics.optics","authors_text":"B. King, W. J. Waters","submitted_at":"2017-05-23T22:42:25Z","abstract_excerpt":"We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08554","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":"1705.08554","created_at":"2026-05-18T00:25:57.646659+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.08554v1","created_at":"2026-05-18T00:25:57.646659+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08554","created_at":"2026-05-18T00:25:57.646659+00:00"},{"alias_kind":"pith_short_12","alias_value":"5RVWE53JAUP6","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5RVWE53JAUP6KKRG","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5RVWE53J","created_at":"2026-05-18T12:31:00.734936+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/5RVWE53JAUP6KKRGFAWQ42IA44","json":"https://pith.science/pith/5RVWE53JAUP6KKRGFAWQ42IA44.json","graph_json":"https://pith.science/api/pith-number/5RVWE53JAUP6KKRGFAWQ42IA44/graph.json","events_json":"https://pith.science/api/pith-number/5RVWE53JAUP6KKRGFAWQ42IA44/events.json","paper":"https://pith.science/paper/5RVWE53J"},"agent_actions":{"view_html":"https://pith.science/pith/5RVWE53JAUP6KKRGFAWQ42IA44","download_json":"https://pith.science/pith/5RVWE53JAUP6KKRGFAWQ42IA44.json","view_paper":"https://pith.science/paper/5RVWE53J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.08554&json=true","fetch_graph":"https://pith.science/api/pith-number/5RVWE53JAUP6KKRGFAWQ42IA44/graph.json","fetch_events":"https://pith.science/api/pith-number/5RVWE53JAUP6KKRGFAWQ42IA44/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5RVWE53JAUP6KKRGFAWQ42IA44/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5RVWE53JAUP6KKRGFAWQ42IA44/action/storage_attestation","attest_author":"https://pith.science/pith/5RVWE53JAUP6KKRGFAWQ42IA44/action/author_attestation","sign_citation":"https://pith.science/pith/5RVWE53JAUP6KKRGFAWQ42IA44/action/citation_signature","submit_replication":"https://pith.science/pith/5RVWE53JAUP6KKRGFAWQ42IA44/action/replication_record"}},"created_at":"2026-05-18T00:25:57.646659+00:00","updated_at":"2026-05-18T00:25:57.646659+00:00"}