Pith Number

pith:7N772ZLB

pith:2012:7N772ZLBF3XU7HZJ4RTSGHGOLQ

not attested not anchored not stored refs pending

Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements

Alexander Hasselhuhn, Carsten Schneider, Fabian Wi{\ss}brock, Jakob Ablinger, Johannes Bl\"umlein, Sebastian Klein

arxiv:1206.2252 v2 · 2012-06-11 · hep-ph · hep-th · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7N772ZLBF3XU7HZJ4RTSGHGOLQ}

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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

2 papers in Pith

SubTropica

The four-loop non-singlet splitting functions in QCD

Receipt and verification

First computed	2026-05-18T01:56:59.884443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb7ffd65612eef4f9f29e467231cce5c23329dccbf2b54793942b241c2241ada

Aliases

arxiv: 1206.2252 · arxiv_version: 1206.2252v2 · doi: 10.48550/arxiv.1206.2252 · pith_short_12: 7N772ZLBF3XU · pith_short_16: 7N772ZLBF3XU7HZJ · pith_short_8: 7N772ZLB

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/7N772ZLBF3XU7HZJ4RTSGHGOLQ \
  | 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: fb7ffd65612eef4f9f29e467231cce5c23329dccbf2b54793942b241c2241ada

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "185f99dae6b0b525f13dafc4f52bcd64d3e4698ab66bc9acede8b947e890e33e",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2012-06-11T15:19:40Z",
    "title_canon_sha256": "b65cc64498c06b90e6443426105d997854995d6464f2cf1e997d53a65fbdd9e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.2252",
    "kind": "arxiv",
    "version": 2
  }
}