Pith Number

pith:LPFDSN32

pith:2001:LPFDSN32DADB65SV3CLEJU3ABX

not attested not anchored not stored refs pending

Three loop gauge beta-function for the most general single gauge-coupling theory

A.G.M. Pickering, D.R.T. Jones, J.A. Gracey

arxiv:hep-ph/0104247 v1 · 2001-04-24 · 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{LPFDSN32DADB65SV3CLEJU3ABX}

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

Novel Phases of a Baryon-Dense QCD-like Theory

Receipt and verification

First computed	2026-07-04T16:27:19.861641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bca39377a18061f7655d89644d3600de23a9b3934c2d07d00ebf4f1c4a01d06

Aliases

arxiv: hep-ph/0104247 · arxiv_version: hep-ph/0104247v1 · doi: 10.48550/arxiv.hep-ph/0104247 · pith_short_12: LPFDSN32DADB · pith_short_16: LPFDSN32DADB65SV · pith_short_8: LPFDSN32

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/LPFDSN32DADB65SV3CLEJU3ABX \
  | 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: 5bca39377a18061f7655d89644d3600de23a9b3934c2d07d00ebf4f1c4a01d06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a3161ed49187cf67cef4cc7d36ad4fe68ee62725892e73dccddcb6127256b7d",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2001-04-24T15:27:39Z",
    "title_canon_sha256": "5fecdcff995577b47e9706d4df90a12f43ebea0c809c19cb9506280ce8263d9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0104247",
    "kind": "arxiv",
    "version": 1
  }
}