Pith Number

pith:DUZNOQ27

pith:1996:DUZNOQ27V42RIXYNWJMJ2C5OJ7

not attested not anchored not stored refs pending

The QCD beta-function at O(1/N_f)

J.A. Gracey

arxiv:hep-ph/9602214 v1 · 1996-02-02 · 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{DUZNOQ27V42RIXYNWJMJ2C5OJ7}

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

2 papers in Pith

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

All-loop four-quark Bethe-Salpeter kernel

Receipt and verification

First computed	2026-07-04T16:01:28.500012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d32d7435faf35145f0db2589d0bae4fe8c6bc600e1a593b81266d82fbc60190

Aliases

arxiv: hep-ph/9602214 · arxiv_version: hep-ph/9602214v1 · doi: 10.48550/arxiv.hep-ph/9602214 · pith_short_12: DUZNOQ27V42R · pith_short_16: DUZNOQ27V42RIXYN · pith_short_8: DUZNOQ27

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/DUZNOQ27V42RIXYNWJMJ2C5OJ7 \
  | 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: 1d32d7435faf35145f0db2589d0bae4fe8c6bc600e1a593b81266d82fbc60190

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a891fcb485f0c90cbb2fb924cecd601f2d7596d41d36524797f878a8401aeafd",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1996-02-02T10:14:11Z",
    "title_canon_sha256": "603aba8b54cdc472602133a5601cc0a3c445f532d2e003a3ebf2587d341770cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9602214",
    "kind": "arxiv",
    "version": 1
  }
}