Pith Number

pith:C6C5E4FN

pith:2021:C6C5E4FNNDD7NO7FIEJNWKLGOX

not attested not anchored not stored refs pending

Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case

Stephen P. Martin

arxiv:2112.07694 v2 · 2021-12-14 · 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{C6C5E4FNNDD7NO7FIEJNWKLGOX}

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	2026-07-05T04:11:53.360679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1785d270ad68c7f6bbe54112db296675f5804a4cd89a4f754bf242dee7523a4f

Aliases

arxiv: 2112.07694 · arxiv_version: 2112.07694v2 · doi: 10.48550/arxiv.2112.07694 · pith_short_12: C6C5E4FNNDD7 · pith_short_16: C6C5E4FNNDD7NO7F · pith_short_8: C6C5E4FN

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/C6C5E4FNNDD7NO7FIEJNWKLGOX \
  | 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: 1785d270ad68c7f6bbe54112db296675f5804a4cd89a4f754bf242dee7523a4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1bb65946b9c2bee4459fd3de36c2f07cbd20b7c304b3342e4d50503fc01be1c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2021-12-14T19:00:10Z",
    "title_canon_sha256": "693e7968ad0238f26bc50150f69e71d8d11ffabfab9f53d59d9494b979aff815"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.07694",
    "kind": "arxiv",
    "version": 2
  }
}