Pith Number

pith:PGZOGECX

pith:2010:PGZOGECXNG5L4OJ33HPSJUYOXT

not attested not anchored not stored refs pending

Beta Function and Anomalous Dimensions

Claudio Pica, Francesco Sannino

arxiv:1011.3832 v2 · 2010-11-16 · hep-ph · hep-lat · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PGZOGECXNG5L4OJ33HPSJUYOXT}

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.

Receipt and verification

First computed	2026-05-18T04:20:24.844062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79b2e3105769babe393bd9df24d30ebcec987194f6188aaa77d923b9a29637c1

Aliases

arxiv: 1011.3832 · arxiv_version: 1011.3832v2 · doi: 10.48550/arxiv.1011.3832 · pith_short_12: PGZOGECXNG5L · pith_short_16: PGZOGECXNG5L4OJ3 · pith_short_8: PGZOGECX

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/PGZOGECXNG5L4OJ33HPSJUYOXT \
  | 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: 79b2e3105769babe393bd9df24d30ebcec987194f6188aaa77d923b9a29637c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f131e720529433eb415e49f6da720236ac4162e25268f32c596df6a41ed380d4",
    "cross_cats_sorted": [
      "hep-lat",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2010-11-16T21:19:41Z",
    "title_canon_sha256": "f66e645307bd46a762e1feb51ebcb406009a96abc5d8fe24fad7a10e14b918bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.3832",
    "kind": "arxiv",
    "version": 2
  }
}