Pith Number

pith:PFYPHTCL

pith:2016:PFYPHTCL7OUYV7KMFXXNF7QHCF

not attested not anchored not stored refs pending

Towards the five-loop Beta function for a general gauge group

Andreas Maier, Peter Marquard, Thomas Luthe, York Schroder

arxiv:1606.08662 v2 · 2016-06-28 · 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{PFYPHTCL7OUYV7KMFXXNF7QHCF}

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

Asymptotic Pad\'e Predictions up to Six Loops in QCD and Eight Loops in $\lambda\phi^4$

Receipt and verification

First computed	2026-05-18T01:10:28.780454Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7970f3cc4bfba98afd4c2deed2fe07117eb5bbe4b8c31560a3e22dfcfaffb916

Aliases

arxiv: 1606.08662 · arxiv_version: 1606.08662v2 · doi: 10.48550/arxiv.1606.08662 · pith_short_12: PFYPHTCL7OUY · pith_short_16: PFYPHTCL7OUYV7KM · pith_short_8: PFYPHTCL

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/PFYPHTCL7OUYV7KMFXXNF7QHCF \
  | 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: 7970f3cc4bfba98afd4c2deed2fe07117eb5bbe4b8c31560a3e22dfcfaffb916

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3038411ef87e42fd2479b0bad2a25e85bb46a60ca980d7215a2e652345cfe0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2016-06-28T11:50:11Z",
    "title_canon_sha256": "237c27bac469d3db2fff7c461908c8dd1faafeb06fa7932632b560ba9b768b4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08662",
    "kind": "arxiv",
    "version": 2
  }
}