Pith Number

pith:KUO7VUAM

pith:2025:KUO7VUAM7EHETBRBNKBHVKDN37

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Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics

Andreas A. Buchheit, Filipp N. Rybakov, Jonathan K. Busse, Torsten Ke{\ss}ler

Infinite lattice sums for dipolar and power-law interactions can be computed exactly using a small direct sum plus zeta function derivative corrections.

arxiv:2509.26274 v3 · 2025-09-30 · math.NA · cond-mat.str-el · cs.NA

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\usepackage{pith}
\pithnumber{KUO7VUAM7EHETBRBNKBHVKDN37}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For general interacting geometries, the exact infinite sum for both dipolar interactions and generalized Riesz power-law potentials can be obtained by complementing a small direct sum by a correction term that involves efficiently computable derivatives of generalized zeta functions.

C2weakest assumption

That the required derivatives of generalized zeta functions (and related special functions such as incomplete Bessel functions) admit a superexponentially convergent algorithm that remains practical and stable for the geometries and derivative orders needed in micromagnetics.

C3one line summary

Zeta-function derivative corrections enable machine-precision evaluation of periodic dipolar and Riesz potentials at the cost of truncated sums.

Receipt and verification

First computed	2026-06-19T16:10:31.462326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

551dfad00cf90e4986216a827aa86ddff3078c1b1d8bff8041813ae856fdc126

Aliases

arxiv: 2509.26274 · arxiv_version: 2509.26274v3 · doi: 10.48550/arxiv.2509.26274 · pith_short_12: KUO7VUAM7EHE · pith_short_16: KUO7VUAM7EHETBRB · pith_short_8: KUO7VUAM

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KUO7VUAM7EHETBRBNKBHVKDN37 \
  | 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: 551dfad00cf90e4986216a827aa86ddff3078c1b1d8bff8041813ae856fdc126

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0777cb5ece166b03e15ebf0a192be6951640df0b723214a08b2cd21977fbac2f",
    "cross_cats_sorted": [
      "cond-mat.str-el",
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-09-30T13:58:28Z",
    "title_canon_sha256": "6aa3cfea5abf1428524d7a6fe27515f933c890ca21ee7b3a0ec66772e2e329a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.26274",
    "kind": "arxiv",
    "version": 3
  }
}