Pith Number

pith:BAGD3QCX

pith:2012:BAGD3QCX4TJ5243DITVA6EOJAB

not attested not anchored not stored refs pending

Multiple Commutator Formulas for Unitary Groups

Nikolai Vavilov, Roozbeh Hazrat, Zuhong Zhang

arxiv:1205.6866 v1 · 2012-05-31 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BAGD3QCX4TJ5243DITVA6EOJAB}

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	2026-05-18T03:49:59.507589Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

080c3dc057e4d3dd736344ea0f11c9005e15ee5f37ce2b527e4dc9d4b06cc799

Aliases

arxiv: 1205.6866 · arxiv_version: 1205.6866v1 · doi: 10.48550/arxiv.1205.6866 · pith_short_12: BAGD3QCX4TJ5 · pith_short_16: BAGD3QCX4TJ5243D · pith_short_8: BAGD3QCX

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/BAGD3QCX4TJ5243DITVA6EOJAB \
  | 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: 080c3dc057e4d3dd736344ea0f11c9005e15ee5f37ce2b527e4dc9d4b06cc799

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4ce5f69b219e9a5549c6d87f43123a3c9e59ae01decdef3b138670cbfd536e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-05-31T01:36:40Z",
    "title_canon_sha256": "acb02d340a6131b057b0547ff8fc74bd090336a430d8c1c75a01944f906be454"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.6866",
    "kind": "arxiv",
    "version": 1
  }
}