Pith Number

pith:MAJCIXIL

pith:2003:MAJCIXILWDK7AQKMIRCYIQMI2I

not attested not anchored not stored refs pending

Renormalization group equations for effective field theories

Gilberto Colangelo, Matthias Buchler

arxiv:hep-ph/0309049 v1 · 2003-09-04 · 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{MAJCIXILWDK7AQKMIRCYIQMI2I}

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

Do $\Lambda_{CC}$ and $G$ run?

Receipt and verification

First computed	2026-07-04T16:40:52.370583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6012245d0bb0d5f0414c4445844188d21812f92a4823fe2725a7050ead73b4f8

Aliases

arxiv: hep-ph/0309049 · arxiv_version: hep-ph/0309049v1 · doi: 10.48550/arxiv.hep-ph/0309049 · pith_short_12: MAJCIXILWDK7 · pith_short_16: MAJCIXILWDK7AQKM · pith_short_8: MAJCIXIL

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/MAJCIXILWDK7AQKMIRCYIQMI2I \
  | 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: 6012245d0bb0d5f0414c4445844188d21812f92a4823fe2725a7050ead73b4f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdf61987d4cc1bc561ed507bbee4d87cb306de644ef4b81cfbec72141997e6e3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-ph",
    "submitted_at": "2003-09-04T16:49:22Z",
    "title_canon_sha256": "50bf929aeb2f8d954655ad1aa76314a195ab9e3020c162b6e7739c3ff578fc81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-ph/0309049",
    "kind": "arxiv",
    "version": 1
  }
}