Pith Number

pith:7GFXRHPQ

pith:2005:7GFXRHPQ2MQW3GLYM6IO3OFUM7

not attested not anchored not stored refs pending

On intertwining operators and finite automorphism groups of vertex operator algebras

Kenichiro Tanabe

arxiv:math/0501312 v1 · 2005-01-20 · 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{7GFXRHPQ2MQW3GLYM6IO3OFUM7}

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	2026-05-18T03:04:22.871812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f98b789df0d3216d99786790edb8b467fa927be051403b15bf1e4cf09da8870c

Aliases

arxiv: math/0501312 · arxiv_version: math/0501312v1 · doi: 10.48550/arxiv.math/0501312 · pith_short_12: 7GFXRHPQ2MQW · pith_short_16: 7GFXRHPQ2MQW3GLY · pith_short_8: 7GFXRHPQ

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/7GFXRHPQ2MQW3GLYM6IO3OFUM7 \
  | 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: f98b789df0d3216d99786790edb8b467fa927be051403b15bf1e4cf09da8870c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "454f55c3b627510a79d88e39f11e3eff27df133874b665b2e46123cc8e718e03",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2005-01-20T01:56:40Z",
    "title_canon_sha256": "97d92908f73b9257572a405abdb3e6eaf2ec8543cf2b8e7fc410a268ae91f73f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0501312",
    "kind": "arxiv",
    "version": 1
  }
}