{"paper":{"title":"Integral representation of time-harmonic solutions to Maxwell's equations with fast numerical convergence","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"Integral representations using assignable distributions yield exponentially convergent approximations to time-harmonic Maxwell solutions.","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.optics","authors_text":"Kalpesh Jaykar, Richard D. James","submitted_at":"2026-05-13T23:06:27Z","abstract_excerpt":"The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \\cite{friesecke_twisted_2016}. Building on an integral form\n  used in \\cite{friesecke_twisted_2016}, we construct integral representations of a broad class of time-harmonic solutions to Maxwell's equations in a vacuum or, more generally, in a homogeneous medium without source terms. The representation includes assignable generalized functions (distributions) that can be tailored to specific boundary or "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we construct integral representations of a broad class of time-harmonic solutions to Maxwell's equations in a vacuum or, more generally, in a homogeneous medium without source terms. ... When the assignable functions satisfy mild periodicity and smoothness conditions, the solutions can be approximated using multi-dimensional trapezoidal rules with exponentially fast convergence.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"When the assignable functions satisfy mild periodicity and smoothness conditions","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Integral representations of Maxwell time-harmonic solutions enable exponentially convergent trapezoidal approximations and constructive interference for icosahedral symmetry.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Integral representations using assignable distributions yield exponentially convergent approximations to time-harmonic Maxwell solutions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9bafa4c6d2bce52bf014f0ca77a7a6ea1d47f4335264ddaddf246718d15656f9"},"source":{"id":"2605.14183","kind":"arxiv","version":1},"verdict":{"id":"ef37c146-30ec-4009-86ef-fb19ccb74739","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:44:16.855182Z","strongest_claim":"we construct integral representations of a broad class of time-harmonic solutions to Maxwell's equations in a vacuum or, more generally, in a homogeneous medium without source terms. ... When the assignable functions satisfy mild periodicity and smoothness conditions, the solutions can be approximated using multi-dimensional trapezoidal rules with exponentially fast convergence.","one_line_summary":"Integral representations of Maxwell time-harmonic solutions enable exponentially convergent trapezoidal approximations and constructive interference for icosahedral symmetry.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"When the assignable functions satisfy mild periodicity and smoothness conditions","pith_extraction_headline":"Integral representations using assignable distributions yield exponentially convergent approximations to time-harmonic Maxwell solutions."},"references":{"count":25,"sample":[{"doi":"","year":2016,"title":"Twisted X-Rays: Incoming Waveforms Yielding Discrete Diffraction Patterns for Helical Structures,","work_id":"0ff47669-c817-4551-bd20-b025700fe0b4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1927,"title":"Plane waves of light,","work_id":"8d812c2a-01f1-4356-9462-8b14956a6084","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1965,"title":"Plane waves in dissipative media,","work_id":"cf50d415-8c82-461f-acc8-5252e8b5acd8","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1953,"title":"P. Morse and H. Feshbach,Methods of Theoretical Physics. International series in pure and applied physics, McGraw-Hill, 1953","work_id":"368720d3-65d9-4149-b761-accacf114a78","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Clemmow,The Plane Wave Spectrum Representation of Electromagnetic Fields: International Series of Monographs in Electromagnetic Waves","work_id":"cc4c6bce-3e6f-4d67-8ca7-97dfbf9c66a6","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":25,"snapshot_sha256":"c96395294969ac1ce465eb364a74c54c9f1959c0f3c4b89ea48dac627ba00520","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"00634329a6b02e711d1ec08412d0bbaf8acde723698ffd68fa3bff58ab1cf098"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}