Pith Number

pith:LSK43KIY

pith:2015:LSK43KIYWV4TOB5V3XOPJHNJF2

not attested not anchored not stored refs pending

Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED

A.L. Kataev (INR RAS, Dolgoprudnyi), Moscow), V.S. Molokoedov (MIPT

arxiv:1507.03547 v3 · 2015-07-13 · hep-ph · 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{LSK43KIYWV4TOB5V3XOPJHNJF2}

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	2026-05-18T01:30:34.239715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c95cda918b5793707b5dddcf49da92e86d1eb261e2cf13426fff7931b0993d7

Aliases

arxiv: 1507.03547 · arxiv_version: 1507.03547v3 · doi: 10.48550/arxiv.1507.03547 · pith_short_12: LSK43KIYWV4T · pith_short_16: LSK43KIYWV4TOB5V · pith_short_8: LSK43KIY

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/LSK43KIYWV4TOB5V3XOPJHNJF2 \
  | 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: 5c95cda918b5793707b5dddcf49da92e86d1eb261e2cf13426fff7931b0993d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24ca9d0056b7f07f2aada0cbc447d261f27126d341ed2529f1b084abe332c6d0",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2015-07-13T18:49:54Z",
    "title_canon_sha256": "7b107984074af91e000c0311e7357265e5b3b59d68e8b68a8976207fcaaa2083"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03547",
    "kind": "arxiv",
    "version": 3
  }
}