Pith Number

pith:NZBRSMGC

pith:2015:NZBRSMGCIYL72DYXTO7LX356WH

not attested not anchored not stored refs pending

Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra

A. Behring, A. De Freitas, A. von Manteuffel, C. Schneider, J. Ablinger, J. Bl\"umlein

arxiv:1509.08324 v1 · 2015-09-28 · hep-ph · cs.SC · 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{NZBRSMGCIYL72DYXTO7LX356WH}

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 four-loop non-singlet splitting functions in QCD

Receipt and verification

First computed	2026-05-18T01:16:48.400970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e431930c24617fd0f179bbebbefbeb1cb9466369e3ecb20fc8ecca4bd953b2e

Aliases

arxiv: 1509.08324 · arxiv_version: 1509.08324v1 · doi: 10.48550/arxiv.1509.08324 · pith_short_12: NZBRSMGCIYL7 · pith_short_16: NZBRSMGCIYL72DYX · pith_short_8: NZBRSMGC

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/NZBRSMGCIYL72DYXTO7LX356WH \
  | 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: 6e431930c24617fd0f179bbebbefbeb1cb9466369e3ecb20fc8ecca4bd953b2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adf0b86b87a484c10bf6c7d401438d032b3748fd4cb72a80d5d8091ad74a18b9",
    "cross_cats_sorted": [
      "cs.SC",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2015-09-28T14:05:33Z",
    "title_canon_sha256": "67c9ed70f8199adf0736c58a3b24402f3b7af464da6d6c51183ac7aace159934"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08324",
    "kind": "arxiv",
    "version": 1
  }
}