Pith Number

pith:3UOSU3KK

pith:2003:3UOSU3KKUNHYVY6SUXPVD2BPAM

not attested not anchored not stored refs pending

High-precision evaluation of four-loop vacuum bubbles in three dimensions

A. Vuorinen, Y. Schroder

arxiv:hep-ph/0311323 v1 · 2003-11-25 · 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{3UOSU3KKUNHYVY6SUXPVD2BPAM}

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.

Receipt and verification

First computed	2026-05-18T01:06:13.277701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd1d2a6d4aa34f8ae3d2a5df51e82f03326bb50bc937a98c707a95b29aaf0a75

Aliases

arxiv: hep-ph/0311323 · arxiv_version: hep-ph/0311323v1 · doi: 10.48550/arxiv.hep-ph/0311323 · pith_short_12: 3UOSU3KKUNHY · pith_short_16: 3UOSU3KKUNHYVY6S · pith_short_8: 3UOSU3KK

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/3UOSU3KKUNHYVY6SUXPVD2BPAM \
  | 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: dd1d2a6d4aa34f8ae3d2a5df51e82f03326bb50bc937a98c707a95b29aaf0a75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf388700e1e23157b1c7668930c1781f43ed94b66f3233ddbfaa745082e7894e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2003-11-25T15:40:26Z",
    "title_canon_sha256": "ff2d75ca45debfc8afaead51f65f24bae0e4c13c64bfca72a1d9f4eac6db1fdc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0311323",
    "kind": "arxiv",
    "version": 1
  }
}