Pith Number

pith:IKBN3UVN

pith:2014:IKBN3UVNF4U7UNJ63X6DCYCYOG

not attested not anchored not stored refs pending

The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System

Jeffrey A. Harvey, John F. R. Duncan

arxiv:1412.8191 v1 · 2014-12-28 · math.RT · hep-th · 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{IKBN3UVNF4U7UNJ63X6DCYCYOG}

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	2026-05-18T00:42:33.566903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4282ddd2ad2f29fa353eddfc31605871976335cd08d93d0c1ba9bd3b4902a83f

Aliases

arxiv: 1412.8191 · arxiv_version: 1412.8191v1 · doi: 10.48550/arxiv.1412.8191 · pith_short_12: IKBN3UVNF4U7 · pith_short_16: IKBN3UVNF4U7UNJ6 · pith_short_8: IKBN3UVN

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/IKBN3UVNF4U7UNJ63X6DCYCYOG \
  | 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: 4282ddd2ad2f29fa353eddfc31605871976335cd08d93d0c1ba9bd3b4902a83f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fac44d2caec42b11c619e2491c1ef6f53ecf9c23055a98b7aba838a8590bf65c",
    "cross_cats_sorted": [
      "hep-th",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2014-12-28T17:34:03Z",
    "title_canon_sha256": "1b0d9f62304e45397900f4aa00be509d72bf70fc966ec91803c8dc62e54e8a56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8191",
    "kind": "arxiv",
    "version": 1
  }
}