Pith Number

pith:VH36RUUY

pith:2009:VH36RUUYJKSODPSNWGP5U7YORL

not attested not anchored not stored refs pending

The orthogonal Weingarten formula in compact form

Teodor Banica

arxiv:0906.4694 v3 · 2009-06-25 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VH36RUUYJKSODPSNWGP5U7YORL}

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	2026-05-18T02:13:12.743375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9f7e8d2984aa4e1be4db19fda7f0e8ae88d1aac28a5311e6b3dc01f3468b205

Aliases

arxiv: 0906.4694 · arxiv_version: 0906.4694v3 · doi: 10.48550/arxiv.0906.4694 · pith_short_12: VH36RUUYJKSO · pith_short_16: VH36RUUYJKSODPSN · pith_short_8: VH36RUUY

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/VH36RUUYJKSODPSNWGP5U7YORL \
  | 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: a9f7e8d2984aa4e1be4db19fda7f0e8ae88d1aac28a5311e6b3dc01f3468b205

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a95220a3f2161747ea175d640e7296689e2f104d0bcdc361cfa5c3238edaf817",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-06-25T13:54:12Z",
    "title_canon_sha256": "d57e2c83d9dad7faedfe4dbf324874a4f836508f9401a3fd6fd9ac341228194c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.4694",
    "kind": "arxiv",
    "version": 3
  }
}