Pith Number

pith:QVZOJHXR

pith:2026:QVZOJHXRJDROQBA6276I7VB5Y3

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Integral representation of time-harmonic solutions to Maxwell's equations with fast numerical convergence

Kalpesh Jaykar, Richard D. James

Integral representations using assignable distributions yield exponentially convergent approximations to time-harmonic Maxwell solutions.

arxiv:2605.14183 v1 · 2026-05-13 · physics.optics · math-ph · math.MP

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Claims

C1strongest 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.

C2weakest assumption

When the assignable functions satisfy mild periodicity and smoothness conditions

C3one line summary

Integral representations of Maxwell time-harmonic solutions enable exponentially convergent trapezoidal approximations and constructive interference for icosahedral symmetry.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] Twisted X-Rays: Incoming Waveforms Yielding Discrete Diffraction Patterns for Helical Structures, 2016

[2] Plane waves of light, 1927

[3] Plane waves in dissipative media, 1965

[4] P. Morse and H. Feshbach,Methods of Theoretical Physics. International series in pure and applied physics, McGraw-Hill, 1953 1953

[5] Clemmow,The Plane Wave Spectrum Representation of Electromagnetic Fields: International Series of Monographs in Electromagnetic Waves 2013

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:11.227063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8572e49ef148e2e8041ed7fc8fd43dc6dd239918b8459046742d75ed24db972a

Aliases

arxiv: 2605.14183 · arxiv_version: 2605.14183v1 · doi: 10.48550/arxiv.2605.14183 · pith_short_12: QVZOJHXRJDRO · pith_short_16: QVZOJHXRJDROQBA6 · pith_short_8: QVZOJHXR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QVZOJHXRJDROQBA6276I7VB5Y3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8572e49ef148e2e8041ed7fc8fd43dc6dd239918b8459046742d75ed24db972a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1984fa4c1b446f1587f4d251ee64a6476be0ca886e93e847120a544f8b7b3ace",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2026-05-13T23:06:27Z",
    "title_canon_sha256": "e865ead309d70e2398f472de00dcd75b2c84844c8dcd3938bdaf212be8391dc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14183",
    "kind": "arxiv",
    "version": 1
  }
}