Pith Number

pith:Z4GV23PA

pith:2016:Z4GV23PAPECE27Q3J5XZ4ZRMMC

not attested not anchored not stored refs pending

Matrix models for multilevel Heckman-Opdam and multivariate Bessel measures

Yi Sun

arxiv:1609.09096 v1 · 2016-09-28 · math.PR · math-ph · math.MP · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z4GV23PAPECE27Q3J5XZ4ZRMMC}

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.

Cited by

1 paper in Pith

Airy$_\beta$ line ensemble and its Laplace transform

Receipt and verification

First computed	2026-05-18T01:03:40.240938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf0d5d6de079044d7e1b4f6f9e662c60b2e63a265b501dd58f3efa2944b04fd7

Aliases

arxiv: 1609.09096 · arxiv_version: 1609.09096v1 · doi: 10.48550/arxiv.1609.09096 · pith_short_12: Z4GV23PAPECE · pith_short_16: Z4GV23PAPECE27Q3 · pith_short_8: Z4GV23PA

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/Z4GV23PAPECE27Q3J5XZ4ZRMMC \
  | 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: cf0d5d6de079044d7e1b4f6f9e662c60b2e63a265b501dd58f3efa2944b04fd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77fffedeee228838bca64d1e0e90cf92c0047cd7089fc19066d5f1c85927ac92",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-28T20:02:56Z",
    "title_canon_sha256": "1abcf31d6d159a09fd34be886d85dfe56fec5f7ca6b35c07b5f4a93b4d079c4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.09096",
    "kind": "arxiv",
    "version": 1
  }
}