Pith Number

pith:4WSNOLPD

pith:2002:4WSNOLPD64FHBESLHBHGJHIIQY

not attested not anchored not stored refs pending

Modular invariance of vertex operator algebras satisfying C_2-cofiniteness

Masahiko Miyamoto (University of Tsukuba)

arxiv:math/0209101 v2 · 2002-09-10 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4WSNOLPD64FHBESLHBHGJHIIQY}

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.

Cited by

1 paper in Pith

Complex Conformal Manifolds

Receipt and verification

First computed	2026-07-04T14:36:25.671602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5a4d72de3f70a70924b384e649d08862aa42ef583d5a3fbc225357f675e93a7

Aliases

arxiv: math/0209101 · arxiv_version: math/0209101v2 · doi: 10.48550/arxiv.math/0209101 · pith_short_12: 4WSNOLPD64FH · pith_short_16: 4WSNOLPD64FHBESL · pith_short_8: 4WSNOLPD

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/4WSNOLPD64FHBESLHBHGJHIIQY \
  | 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: e5a4d72de3f70a70924b384e649d08862aa42ef583d5a3fbc225357f675e93a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbc72acb87e5fbdf024b2802b97a5521d4734bff14022ea2b0f8589c729a74e5",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2002-09-10T01:47:26Z",
    "title_canon_sha256": "669e132d33245feaa3d83050e3800e0241dae9e615b85ba9862460cb29751b48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0209101",
    "kind": "arxiv",
    "version": 2
  }
}