Pith Number

pith:HCZJ53CG

pith:2021:HCZJ53CG32Q42ZQBCFYUNKPMOP

not attested not anchored not stored refs pending

General Gauge-Yukawa-Quartic $\beta$-Functions at 4-3-2--Loop Order

Anders Eller Thomsen, Florian Herren, Joshua Davies

arxiv:2110.05496 v1 · 2021-10-11 · hep-ph · 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{HCZJ53CG32Q42ZQBCFYUNKPMOP}

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	2026-07-05T03:51:33.718445Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38b29eec46dea1cd6601117146a9ec73f9036ee3135e4b9c24e8b48b230917be

Aliases

arxiv: 2110.05496 · arxiv_version: 2110.05496v1 · doi: 10.48550/arxiv.2110.05496 · pith_short_12: HCZJ53CG32Q4 · pith_short_16: HCZJ53CG32Q42ZQB · pith_short_8: HCZJ53CG

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/HCZJ53CG32Q42ZQBCFYUNKPMOP \
  | 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: 38b29eec46dea1cd6601117146a9ec73f9036ee3135e4b9c24e8b48b230917be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "324f242a21094e3bab8ab71238a848c9cd45623725d5afd474f4481a0de7e4cc",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2021-10-11T18:00:01Z",
    "title_canon_sha256": "b697e0cbe2cff67cf672444c6be8d8db76ad9185094b208699c891f78887f524"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.05496",
    "kind": "arxiv",
    "version": 1
  }
}