Pith Number

pith:AI2SPDJN

pith:2026:AI2SPDJNYGLWMXH5XFDFCGNRCT

not attested not anchored not stored refs pending

Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions

Tatsuhiro Misumi

A neural network trained to satisfy the Ginsparg-Wilson relation as a soft constraint reproduces the overlap fermion operator to high accuracy without explicit sign-function approximations.

arxiv:2605.06022 v3 · 2026-05-07 · hep-lat · hep-th

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4 Citations open

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Claims

C1strongest claim

when trained to satisfy the Ginsparg-Wilson (GW) relation as a soft constraint, a neural network reproduces the overlap fermion operator to high numerical accuracy and learns an effective sign-function mapping without explicitly using a prescribed polynomial or rational approximation. [...] by changing the initial search bias, the same framework also finds a distinct solution corresponding to a Fujikawa-type generalized GW relation.

C2weakest assumption

That training the neural network with the Ginsparg-Wilson relation as a soft constraint will lead to the physically correct continuum limit and correct behavior for all relevant momenta, without additional verification steps or hard enforcement of locality.

C3one line summary

Physics-Informed Neural Networks construct lattice Dirac operators satisfying the Ginsparg-Wilson relation, reproducing overlap fermions to high accuracy and discovering a Fujikawa-type generalized relation via algebraic search.

Cited by

1 paper in Pith

Higher-order hopping-parameter expansion by human-AI collaboration

Receipt and verification

First computed	2026-06-25T01:18:38.379300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0235278d2dc197665cfdb9465119b114f8baeb5d032008c2c9a26c700beecca8

Aliases

arxiv: 2605.06022 · arxiv_version: 2605.06022v3 · doi: 10.48550/arxiv.2605.06022 · pith_short_12: AI2SPDJNYGLW · pith_short_16: AI2SPDJNYGLWMXH5 · pith_short_8: AI2SPDJN

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AI2SPDJNYGLWMXH5XFDFCGNRCT \
  | 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: 0235278d2dc197665cfdb9465119b114f8baeb5d032008c2c9a26c700beecca8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d078ccbe4c4c87a7ccfe7e3057aeeafbd814f7f2e888e4dc3c4aab33fd739f3",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-lat",
    "submitted_at": "2026-05-07T11:15:43Z",
    "title_canon_sha256": "044587b378b747012ed51d07487f71dc1f109172a4f5d020c4049f36dfa141ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06022",
    "kind": "arxiv",
    "version": 3
  }
}