Pith Number

pith:T2RBUVEI

pith:2021:T2RBUVEIBRX3TYL2OSID4LU2L3

not attested not anchored not stored refs pending

Four-Loop Gauge and Three-Loop Yukawa Beta-Functions in a General Renormalizable Theory

Alexander Bednyakov, Andrey Pikelner

arxiv:2105.09918 v3 · 2021-05-20 · 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{T2RBUVEIBRX3TYL2OSID4LU2L3}

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

New Solutions of RG Equations for \alpha_s and y_{top}

Receipt and verification

First computed	2026-07-05T03:01:18.473719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ea21a54880c6fb9e17a74903e2e9a5ee9ae0f3ded0c83b0c96fcd6f131e1e35

Aliases

arxiv: 2105.09918 · arxiv_version: 2105.09918v3 · doi: 10.48550/arxiv.2105.09918 · pith_short_12: T2RBUVEIBRX3 · pith_short_16: T2RBUVEIBRX3TYL2 · pith_short_8: T2RBUVEI

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/T2RBUVEIBRX3TYL2OSID4LU2L3 \
  | 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: 9ea21a54880c6fb9e17a74903e2e9a5ee9ae0f3ded0c83b0c96fcd6f131e1e35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "087d7ef15606b00da18c7731efc106964a46850d383a50598e3ef279bcf05765",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2021-05-20T17:29:20Z",
    "title_canon_sha256": "e748448fb0061776bddd1744b0950ac9ce68138bd84821da30a8d02f5dfc6831"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.09918",
    "kind": "arxiv",
    "version": 3
  }
}