Pith Number

pith:HAC4MTKP

pith:1996:HAC4MTKPUBSLTCRP3UCNIEUVDY

not attested not anchored not stored refs pending

A Prediction for the 4-Loop \beta Function

John Ellis (CERN), Marek Karliner (Tel-Aviv Univ.), Mark. A. Samuel (McGill, SLAC)

arxiv:hep-ph/9612202 v3 · 1996-11-29 · hep-ph · cond-mat.stat-mech · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HAC4MTKPUBSLTCRP3UCNIEUVDY}

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

1 paper in Pith

Asymptotic Pad\'e Predictions up to Six Loops in QCD and Eight Loops in $\lambda\phi^4$

Receipt and verification

First computed	2026-05-18T01:06:09.817872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3805c64d4fa064b98a2fdd04d412951e04421f571acebb05f4c59bbbe37d87e9

Aliases

arxiv: hep-ph/9612202 · arxiv_version: hep-ph/9612202v3 · doi: 10.48550/arxiv.hep-ph/9612202 · pith_short_12: HAC4MTKPUBSL · pith_short_16: HAC4MTKPUBSLTCRP · pith_short_8: HAC4MTKP

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/HAC4MTKPUBSLTCRP3UCNIEUVDY \
  | 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: 3805c64d4fa064b98a2fdd04d412951e04421f571acebb05f4c59bbbe37d87e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e68d6b0d4438c56626e7ff0506bf131886dd77a297ee58b5eac90a62f4358343",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1996-11-29T10:23:54Z",
    "title_canon_sha256": "63133a22f47dd4e645e767594d72a8706d9d9da71e5e0e71aab260b9156cfb86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9612202",
    "kind": "arxiv",
    "version": 3
  }
}