Pith Number

pith:7B5M25WO

pith:2015:7B5M25WOMKTUQNBFZ5CVSDQOU5

not attested not anchored not stored refs pending

Proof of the Umbral Moonshine Conjecture

John F. R. Duncan, Ken Ono, Michael J. Griffin

arxiv:1503.01472 v2 · 2015-03-04 · math.RT · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7B5M25WOMKTUQNBFZ5CVSDQOU5}

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	2026-05-18T01:23:38.477921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f87acd76ce62a7483425cf45590e0ea759aa2c6d2aecf352916276c13db6f228

Aliases

arxiv: 1503.01472 · arxiv_version: 1503.01472v2 · doi: 10.48550/arxiv.1503.01472 · pith_short_12: 7B5M25WOMKTU · pith_short_16: 7B5M25WOMKTUQNBF · pith_short_8: 7B5M25WO

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/7B5M25WOMKTUQNBFZ5CVSDQOU5 \
  | 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: f87acd76ce62a7483425cf45590e0ea759aa2c6d2aecf352916276c13db6f228

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbdcb730eecfeeaf7cfbb1ec0123c0f7cfbe7e72c2cb31183af9905f25200eaa",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-03-04T21:03:46Z",
    "title_canon_sha256": "a5a663f145a9bde686dc1902af6f347594791fd9d8c872513b4d35edbc9925fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.01472",
    "kind": "arxiv",
    "version": 2
  }
}