Pith Number

pith:D3KBO77K

pith:2013:D3KBO77KLY24TSB5YDAPQIRCSG

not attested not anchored not stored refs pending

Higher-Loop Structural Properties of the $\beta$ Function in Asymptotically Free Vectorial Gauge Theories

Robert Shrock

arxiv:1301.3209 v1 · 2013-01-15 · 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{D3KBO77KLY24TSB5YDAPQIRCSG}

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	2026-05-18T03:26:12.125651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ed4177fea5e35c9c83dc0c0f8222291a957df351daa48ac6810b69447ec2ee0

Aliases

arxiv: 1301.3209 · arxiv_version: 1301.3209v1 · doi: 10.48550/arxiv.1301.3209 · pith_short_12: D3KBO77KLY24 · pith_short_16: D3KBO77KLY24TSB5 · pith_short_8: D3KBO77K

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/D3KBO77KLY24TSB5YDAPQIRCSG \
  | 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: 1ed4177fea5e35c9c83dc0c0f8222291a957df351daa48ac6810b69447ec2ee0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48ceda8baca846489c3c46b93f625233caaba330e905a907a1478ed6b2c07a1c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2013-01-15T02:51:26Z",
    "title_canon_sha256": "7d3adf0b609f65d8f25990bc85b4972054f273440c0970ec40a2409a8c3d220b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.3209",
    "kind": "arxiv",
    "version": 1
  }
}