Pith Number

pith:BMAPZNAG

pith:2019:BMAPZNAGCTYZVREWYSYWWQ3MIF

not attested not anchored not stored refs pending

Gauge coupling beta functions to four-loop order in the Standard Model

Anders Eller Thomsen, Colin Poole, Florian Herren, Joshua Davies, Matthias Steinhauser

arxiv:1912.07624 v1 · 2019-12-16 · 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{BMAPZNAGCTYZVREWYSYWWQ3MIF}

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

Three-loop corrections to the Fermi decay constant in the $\overline{\rm{MS}}$ scheme

Receipt and verification

First computed	2026-07-05T00:43:43.970297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b00fcb40614f19ac496c4b16b436c417bb44f363c929d4a7ce85157513f6332

Aliases

arxiv: 1912.07624 · arxiv_version: 1912.07624v1 · doi: 10.48550/arxiv.1912.07624 · pith_short_12: BMAPZNAGCTYZ · pith_short_16: BMAPZNAGCTYZVREW · pith_short_8: BMAPZNAG

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/BMAPZNAGCTYZVREWYSYWWQ3MIF \
  | 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: 0b00fcb40614f19ac496c4b16b436c417bb44f363c929d4a7ce85157513f6332

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b1d3658db589439b7f95e6747c1524df646e4d6d94d30e33b4012019480386b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2019-12-16T19:00:08Z",
    "title_canon_sha256": "d96b379a9a91c84a9781e2a33761fdf276cfaf4191ba2cdddc9c9d65de9079f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.07624",
    "kind": "arxiv",
    "version": 1
  }
}