Pith Number

pith:STGCGAGC

pith:2004:STGCGAGCVFIAJ5I4QELQFDHQLX

not attested not anchored not stored refs pending

Integration with respect to the Haar measure on unitary, orthogonal and symplectic group

Benoit Collins, Piotr Sniady

arxiv:math-ph/0402073 v1 · 2004-02-26 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{STGCGAGCVFIAJ5I4QELQFDHQLX}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-17T23:52:34.636576Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94cc2300c2a95004f51c8117028cf05dc3bc35a953aaf153061b6f13fd953964

Aliases

arxiv: math-ph/0402073 · arxiv_version: math-ph/0402073v1 · doi: 10.48550/arxiv.math-ph/0402073 · pith_short_12: STGCGAGCVFIA · pith_short_16: STGCGAGCVFIAJ5I4 · pith_short_8: STGCGAGC

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/STGCGAGCVFIAJ5I4QELQFDHQLX \
  | 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: 94cc2300c2a95004f51c8117028cf05dc3bc35a953aaf153061b6f13fd953964

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7055788b17a795600d5685d99003b737d03db5a48d03cbfce433c92ccbb26da3",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2004-02-26T08:15:59Z",
    "title_canon_sha256": "9e92439068fd1f9d408980ce5b7a57502016bba7fc11a56df7036decf048ca96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0402073",
    "kind": "arxiv",
    "version": 1
  }
}