Pith Number

pith:U6RA5YRG

pith:2009:U6RA5YRGJDDBT6RBWYRJAFAX5P

not attested not anchored not stored refs pending

The Massive Soft Anomalous Dimension Matrix at Two Loops

Alexander Mitov, George Sterman, Ilmo Sung

arxiv:0903.3241 v2 · 2009-03-19 · 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{U6RA5YRGJDDBT6RBWYRJAFAX5P}

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

Soft Factorisation and Exponentiation from Schwinger-Space Geometry

Receipt and verification

First computed	2026-07-04T15:44:00.630851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7a20ee22648c619fa21b622901417ebe9be93e3c2d989e5a1a613a9153e7b21

Aliases

arxiv: 0903.3241 · arxiv_version: 0903.3241v2 · doi: 10.48550/arxiv.0903.3241 · pith_short_12: U6RA5YRGJDDB · pith_short_16: U6RA5YRGJDDBT6RB · pith_short_8: U6RA5YRG

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/U6RA5YRGJDDBT6RBWYRJAFAX5P \
  | 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: a7a20ee22648c619fa21b622901417ebe9be93e3c2d989e5a1a613a9153e7b21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d995a0b69154763f388e28fd8a6ced500295e59202ad840cea8fd60432fb5aba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2009-03-19T15:25:32Z",
    "title_canon_sha256": "436d74830ce2c17a79e3a564c9a4d964483487a87ecfb6e034812deb127379d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.3241",
    "kind": "arxiv",
    "version": 2
  }
}