Pith Number

pith:SFXL6YVH

pith:1997:SFXL6YVH6JYAXVPJAGY6OWZC3G

not attested not anchored not stored refs pending

Beta functions and anomalous dimensions up to three loops

Konstantin Chetyrkin, Manfred Muenz, Mikolaj Misiak

arxiv:hep-ph/9711266 v1 · 1997-11-08 · hep-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SFXL6YVH6JYAXVPJAGY6OWZC3G}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Cited by

4 papers in Pith

Smooth Threshold Effects from Dimensional Regularization

Pseudo-Evanescent Feynman Integrals from Local Subtraction

Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion

Four-loop QCD mixing of current-current operators

Receipt and verification

First computed	2026-07-04T16:05:17.422928Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

916ebf62a7f2700bd5e901b1e75b22d99c05bbab158dd9103b8ca9ce3c19fa36

Aliases

arxiv: hep-ph/9711266 · arxiv_version: hep-ph/9711266v1 · doi: 10.48550/arxiv.hep-ph/9711266 · pith_short_12: SFXL6YVH6JYA · pith_short_16: SFXL6YVH6JYAXVPJ · pith_short_8: SFXL6YVH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SFXL6YVH6JYAXVPJAGY6OWZC3G \
  | 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: 916ebf62a7f2700bd5e901b1e75b22d99c05bbab158dd9103b8ca9ce3c19fa36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "622f3d283ee57cd12dec786e91fc177bd64d9bd9ac23f2e8f95faefd28035195",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1997-11-08T10:35:37Z",
    "title_canon_sha256": "1023eb8c93645f4b59c827e4bb3326bfae2bbaf09d27de3975d0c9815a0a79e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9711266",
    "kind": "arxiv",
    "version": 1
  }
}