Pith Number

pith:ZKAF2SNA

pith:2011:ZKAF2SNAJPZFWYIJGE35KLB2BG

not attested not anchored not stored refs pending

Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops

Stanley J. Brodsky, Xing-Gang Wu

arxiv:1111.6175 v5 · 2011-11-26 · 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{ZKAF2SNAJPZFWYIJGE35KLB2BG}

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

Renormalisation

Receipt and verification

First computed	2026-05-18T02:22:30.358294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca805d49a04bf25b61093137d52c3a098fff27669893203270cf09a2d77eb9a6

Aliases

arxiv: 1111.6175 · arxiv_version: 1111.6175v5 · doi: 10.48550/arxiv.1111.6175 · pith_short_12: ZKAF2SNAJPZF · pith_short_16: ZKAF2SNAJPZFWYIJ · pith_short_8: ZKAF2SNA

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/ZKAF2SNAJPZFWYIJGE35KLB2BG \
  | 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: ca805d49a04bf25b61093137d52c3a098fff27669893203270cf09a2d77eb9a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9b7bcebfbf92325225dd3f36b12f57c77ae0a784a4e88ae107ad5ef33453a7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2011-11-26T16:58:16Z",
    "title_canon_sha256": "968b9abc0031401e21a4f2a4b74f81184d05b9f28a08a3f0ee3dde24c196d7ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6175",
    "kind": "arxiv",
    "version": 5
  }
}