Pith Number

pith:42LNIHLK

pith:1997:42LNIHLK2NPFWWRZ75EFR5LMEZ

not attested not anchored not stored refs pending

The Running Gauge Coupling in the Exact Renormalization Group Approach

Ulrich Ellwanger

arxiv:hep-ph/9702309 v1 · 1997-02-12 · 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{42LNIHLK2NPFWWRZ75EFR5LMEZ}

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	2026-07-04T14:30:09.309480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e696d41d6ad35e5b5a39ff4858f56c265d4cf3851c111eeedb66fd03ec95de35

Aliases

arxiv: hep-ph/9702309 · arxiv_version: hep-ph/9702309v1 · doi: 10.48550/arxiv.hep-ph/9702309 · pith_short_12: 42LNIHLK2NPF · pith_short_16: 42LNIHLK2NPFWWRZ · pith_short_8: 42LNIHLK

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/42LNIHLK2NPFWWRZ75EFR5LMEZ \
  | 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: e696d41d6ad35e5b5a39ff4858f56c265d4cf3851c111eeedb66fd03ec95de35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4336b8c2028755ca54c3f9112cacc0d8b8282ac92b4705366807e423d3c3518c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "1997-02-12T10:18:55Z",
    "title_canon_sha256": "7284132f757cd387c82cc19ad8c63fe85a8aa8b6d49929ab637877cc4b76da01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/9702309",
    "kind": "arxiv",
    "version": 1
  }
}