Pith Number

pith:MTTQRM5D

pith:2005:MTTQRM5DYDUCHO6GASM77OOAJY

not attested not anchored not stored refs pending

High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles

A. Vuorinen, Y. Schroder

arxiv:hep-ph/0503209 v1 · 2005-03-21 · 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{MTTQRM5DYDUCHO6GASM77OOAJY}

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	2026-07-04T16:55:38.078666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64e708b3a3c0e823bbc60499ffb9c04e38930526c42dce8022043c3a3b7f377c

Aliases

arxiv: hep-ph/0503209 · arxiv_version: hep-ph/0503209v1 · doi: 10.48550/arxiv.hep-ph/0503209 · pith_short_12: MTTQRM5DYDUC · pith_short_16: MTTQRM5DYDUCHO6G · pith_short_8: MTTQRM5D

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/MTTQRM5DYDUCHO6GASM77OOAJY \
  | 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: 64e708b3a3c0e823bbc60499ffb9c04e38930526c42dce8022043c3a3b7f377c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97c4c60ac513e1181e79dd88862e1cc31d8caf4cfa6956b00cd7c9e258ac5cb2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2005-03-21T21:09:56Z",
    "title_canon_sha256": "c123246bae4bcf8bfe10fc9daea49eabb725099f88e0b3cb5abb4b4abed6327d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0503209",
    "kind": "arxiv",
    "version": 1
  }
}