Pith Number

pith:XQHRZPEP

pith:2019:XQHRZPEPS5JFMX6DS6B3UEJ2XH

not attested not anchored not stored refs pending

The Brown measure of the free multiplicative Brownian motion

Brian C. Hall, Bruce K. Driver, Todd Kemp

arxiv:1903.11015 v3 · 2019-03-26 · math.PR · hep-th · math-ph · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XQHRZPEPS5JFMX6DS6B3UEJ2XH}

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

Brown Measures of Free Circular and Multiplicative Brownian Motions with Self-Adjoint and Unitary Initial Conditions

Receipt and verification

First computed	2026-07-05T06:37:08.677784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc0f1cbc8f9752565fc39783ba113ab9cd4ebd7ec47594d1fd910172a7aabba6

Aliases

arxiv: 1903.11015 · arxiv_version: 1903.11015v3 · doi: 10.48550/arxiv.1903.11015 · pith_short_12: XQHRZPEPS5JF · pith_short_16: XQHRZPEPS5JFMX6D · pith_short_8: XQHRZPEP

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/XQHRZPEPS5JFMX6DS6B3UEJ2XH \
  | 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: bc0f1cbc8f9752565fc39783ba113ab9cd4ebd7ec47594d1fd910172a7aabba6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "549c644bc2d8bd58253cb36653df44acc156d280621a7a4dcd1e1db8bb04ba19",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-03-26T16:53:24Z",
    "title_canon_sha256": "489726fd94d471f1c27c535133b026d2c38dfdd0e7173f6f8c9ea34ca4077c53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.11015",
    "kind": "arxiv",
    "version": 3
  }
}