Pith Number

pith:CZLNMVVY

pith:2015:CZLNMVVYX6V55NAGFL3DUAOW4B

not attested not anchored not stored refs pending

Genus Two Zhu Theory for Vertex Operator Algebras

Michael P. Tuite, Thomas Gilroy

arxiv:1511.07664 v3 · 2015-11-24 · math.QA · hep-th · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CZLNMVVYX6V55NAGFL3DUAOW4B}

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	2026-05-18T01:01:08.731621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1656d656b8bfabdeb4062af63a01d6e0687a8a867f63a73478b6e7d58137c877

Aliases

arxiv: 1511.07664 · arxiv_version: 1511.07664v3 · doi: 10.48550/arxiv.1511.07664 · pith_short_12: CZLNMVVYX6V5 · pith_short_16: CZLNMVVYX6V55NAG · pith_short_8: CZLNMVVY

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/CZLNMVVYX6V55NAGFL3DUAOW4B \
  | 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: 1656d656b8bfabdeb4062af63a01d6e0687a8a867f63a73478b6e7d58137c877

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fdb3edf4cfcc02c5ff785fda99ad697880c5aca6c6eaab59f7e0d44cab61877",
    "cross_cats_sorted": [
      "hep-th",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-11-24T11:54:33Z",
    "title_canon_sha256": "579a27a724a449c12cfb762e42e8968ccbffb5cc42b1c66ed2413a1fb226d486"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07664",
    "kind": "arxiv",
    "version": 3
  }
}