Pith Number

pith:LETZOIVP

pith:2006:LETZOIVPMJHSRNHIGJYM6CI3A2

not attested not anchored not stored refs pending

Four-Loop Anomalous Dimensions for Radiative Flavour-Changing Decays

Michal Czakon, Mikolaj Misiak, Ulrich Haisch

arxiv:hep-ph/0612329 v1 · 2006-12-27 · 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{LETZOIVPMJHSRNHIGJYM6CI3A2}

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

The photon-energy spectrum in $B\to X_s\gamma$ to N$^3$LO: light-fermion and large-$N_{\rm c}$ corrections

Receipt and verification

First computed	2026-05-18T04:38:27.132646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59279722af624f28b4e83270cf091b06affeaccd3688965eab074a8e53e382f1

Aliases

arxiv: hep-ph/0612329 · arxiv_version: hep-ph/0612329v1 · doi: 10.48550/arxiv.hep-ph/0612329 · pith_short_12: LETZOIVPMJHS · pith_short_16: LETZOIVPMJHSRNHI · pith_short_8: LETZOIVP

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/LETZOIVPMJHSRNHIGJYM6CI3A2 \
  | 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: 59279722af624f28b4e83270cf091b06affeaccd3688965eab074a8e53e382f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03a8a5ef02e6f026ce4c3bacd5a2452f2017b4bccbd9fafd292d7379a0fff4f2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2006-12-27T16:43:35Z",
    "title_canon_sha256": "3acc4d3184b9ccf9936a3e5e1f28f3fcb8a48244b02a34f175283390a53c547e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0612329",
    "kind": "arxiv",
    "version": 1
  }
}