Pith Number

pith:4IFTPN5P

pith:2002:4IFTPN5P3CJCPMAYNP34DPLYRT

not attested not anchored not stored refs pending

Representations of the twisted Heisenberg-Virasoro algebra at level zero

Yuly Billig

arxiv:math/0201314 v2 · 2002-01-31 · math.RT · 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{4IFTPN5P3CJCPMAYNP34DPLYRT}

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	2026-05-18T03:41:32.627086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e20b37b7afd89227b0186bf7c1bd788cd84fe9e930e162e75cc8cc7021795b93

Aliases

arxiv: math/0201314 · arxiv_version: math/0201314v2 · doi: 10.48550/arxiv.math/0201314 · pith_short_12: 4IFTPN5P3CJC · pith_short_16: 4IFTPN5P3CJCPMAY · pith_short_8: 4IFTPN5P

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/4IFTPN5P3CJCPMAYNP34DPLYRT \
  | 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: e20b37b7afd89227b0186bf7c1bd788cd84fe9e930e162e75cc8cc7021795b93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8aec1b469c138e58ba0c9edee39abc2571800aabf78dd9697595be28afe68b14",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2002-01-31T14:23:49Z",
    "title_canon_sha256": "46849274e4ccbcd2bf08c0ce79a444011b3c67803555a5e0187af7360ec26bcf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0201314",
    "kind": "arxiv",
    "version": 2
  }
}