Pith Number

pith:MQIRIEQP

pith:2004:MQIRIEQPKI3LWFSGCT77NPLUA4

not attested not anchored not stored refs pending

An algebraic Birkhoff decomposition for the continuous renormalization group

F. Girelli, P. Martinetti, T. Krajewski

arxiv:hep-th/0401157 v1 · 2004-01-22 · hep-th · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MQIRIEQPKI3LWFSGCT77NPLUA4}

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	2026-05-18T01:38:46.391695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

641114120f5236bb164614fff6bd74071d35795c8547e9e5fb9988ef5492f3c7

Aliases

arxiv: hep-th/0401157 · arxiv_version: hep-th/0401157v1 · doi: 10.48550/arxiv.hep-th/0401157 · pith_short_12: MQIRIEQPKI3L · pith_short_16: MQIRIEQPKI3LWFSG · pith_short_8: MQIRIEQP

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/MQIRIEQPKI3LWFSGCT77NPLUA4 \
  | 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: 641114120f5236bb164614fff6bd74071d35795c8547e9e5fb9988ef5492f3c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acf2c249c3240cf2c63c75a4cd268bcbc8d475c2164697e7313621b8bebfddd7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2004-01-22T15:16:18Z",
    "title_canon_sha256": "1441ae5127fd15b6b70aedcadf1ac841a877f0bf55947d6ea11de9dfcd374320"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0401157",
    "kind": "arxiv",
    "version": 1
  }
}