Pith Number

pith:WQAGASDD

pith:1992:WQAGASDDTIDTVGITVVGKXH4Y7E

not attested not anchored not stored refs pending

The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: ${\cal O}(\alpha_s^2)$

Andrzej J. Buras, Markus E. Lautenbacher, Matthias Jamin, Peter H. Weisz

arxiv:hep-ph/9211304 v1 · 1992-11-25 · 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{WQAGASDDTIDTVGITVVGKXH4Y7E}

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

3 papers in Pith

Two-Loop Anomalous Dimensions in the LEFT: Dimension-Six Four-Fermion Operators in NDR

Next-to-next-to-leading QCD corrections to the $\mathbf{B^+}$-$\mathbf{B_d^0}$, $\mathbf{D^+}$-$\mathbf{D^0}$, and $\mathbf{D_s^+}$-$\mathbf{D^0}$ lifetime ratios

Four-loop QCD mixing of current-current operators

Receipt and verification

First computed	2026-07-04T15:55:17.866201Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4006048639a073a9913ad4cab9f98f915c9991ab8e0dbb102bf2d741ca06dfd

Aliases

arxiv: hep-ph/9211304 · arxiv_version: hep-ph/9211304v1 · doi: 10.48550/arxiv.hep-ph/9211304 · pith_short_12: WQAGASDDTIDT · pith_short_16: WQAGASDDTIDTVGIT · pith_short_8: WQAGASDD

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/WQAGASDDTIDTVGITVVGKXH4Y7E \
  | 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: b4006048639a073a9913ad4cab9f98f915c9991ab8e0dbb102bf2d741ca06dfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9ce64db4e5ced7f4558205eaadfedefcffdb9016d2300bfd6121cb3fef618e3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1992-11-25T14:03:51Z",
    "title_canon_sha256": "00bb5b09c76702179e6c11513dd1bed667d1d9670423e666fef8d5f3098729d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9211304",
    "kind": "arxiv",
    "version": 1
  }
}