Pith Number

pith:XSPE7WQP

pith:2002:XSPE7WQPDZU3P6W7DIOEOFSF3W

not attested not anchored not stored refs pending

Dualities and vertex operator algebras of affine type

Julius Borcea

arxiv:math/0212177 v1 · 2002-12-12 · math.QA · 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{XSPE7WQPDZU3P6W7DIOEOFSF3W}

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	2026-07-04T14:36:49.567468Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc9e4fda0f1e69b7fadf1a1c471645ddbfe4a2aa5055d13a54db25d1e92f899e

Aliases

arxiv: math/0212177 · arxiv_version: math/0212177v1 · doi: 10.48550/arxiv.math/0212177 · pith_short_12: XSPE7WQPDZU3 · pith_short_16: XSPE7WQPDZU3P6W7 · pith_short_8: XSPE7WQP

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/XSPE7WQPDZU3P6W7DIOEOFSF3W \
  | 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: bc9e4fda0f1e69b7fadf1a1c471645ddbfe4a2aa5055d13a54db25d1e92f899e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab47fcfdf4d599997a4c89cf6831c3213d7fceb352fda2d76fae6f68c94416b7",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2002-12-12T19:37:17Z",
    "title_canon_sha256": "e6a0f24deefe3fe7d3a494306b89112ce9bc1adac5146f8e08133372da67c6f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0212177",
    "kind": "arxiv",
    "version": 1
  }
}