Pith Number

pith:VPJO3CYJ

pith:1998:VPJO3CYJEV4XCVMGS5Q5RO4V5R

not attested not anchored not stored refs pending

Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity

D. J. Broadhurst

arxiv:hep-th/9803091 v1 · 1998-03-11 · hep-th · hep-ph · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPJO3CYJEV4XCVMGS5Q5RO4V5R}

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	2026-05-18T04:13:16.741297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd2ed8b0925797155869761d8bb95ec4723a655de5525ffc1058e237bb6f69d

Aliases

arxiv: hep-th/9803091 · arxiv_version: hep-th/9803091v1 · doi: 10.48550/arxiv.hep-th/9803091 · pith_short_12: VPJO3CYJEV4X · pith_short_16: VPJO3CYJEV4XCVMG · pith_short_8: VPJO3CYJ

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/VPJO3CYJEV4XCVMGS5Q5RO4V5R \
  | 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: abd2ed8b0925797155869761d8bb95ec4723a655de5525ffc1058e237bb6f69d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0280757329d4409a9e896de416b68dc9afe3f782266d741ebc4117ff6def11a",
    "cross_cats_sorted": [
      "hep-ph",
      "math.CA"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "1998-03-11T09:33:09Z",
    "title_canon_sha256": "404369f71f6a8d5f1425bcd5c95203375138540b51d82b4cae7dd48bffa4f21b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/9803091",
    "kind": "arxiv",
    "version": 1
  }
}