Pith Number

pith:7QCLGA53

pith:2026:7QCLGA53ZDUEICV5IZWALZRYTO

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Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part

B.A. Kniehl, V.N. Velizhanin

The term proportional to zeta(3) in the four-loop non-singlet twist-two quark anomalous dimension is given in closed form for arbitrary Lorentz spin N.

arxiv:2605.10284 v2 · 2026-05-11 · hep-ph

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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

we present its term proportional to zeta(3) in closed form. These results have been extracted from published Mellin moments, for N=1,...,16 and N=3,...,15, respectively, by analytic reconstruction using advanced methods of number theory.

C2weakest assumption

The analytic reconstruction from a finite set of Mellin moments (N up to 16) yields the exact closed-form expression valid for all N, with no additional transcendental structures or gauge-group dependencies missed by the number-theory method.

C3one line summary

Closed-form expression for the ζ(3) term of the four-loop non-singlet twist-two quark anomalous dimension for arbitrary N, extracted via analytic reconstruction from Mellin moments.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-01T02:03:43.147275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc04b303bbc8e8440abd466c05e6389b97414a6e3a2be797c1ca038375f61492

Aliases

arxiv: 2605.10284 · arxiv_version: 2605.10284v2 · doi: 10.48550/arxiv.2605.10284 · pith_short_12: 7QCLGA53ZDUE · pith_short_16: 7QCLGA53ZDUEICV5 · pith_short_8: 7QCLGA53

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7QCLGA53ZDUEICV5IZWALZRYTO \
  | 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: fc04b303bbc8e8440abd466c05e6389b97414a6e3a2be797c1ca038375f61492

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f867e90f0d956861b3ed5af14268a7425be8cecd561b6c1593764d755e8080c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-05-11T09:44:34Z",
    "title_canon_sha256": "3fe40d8432e92b21053f1a69766b1e8c6b51623673d875c75fd60fe0abd9dae3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10284",
    "kind": "arxiv",
    "version": 2
  }
}