Pith Number

pith:ZCBURDMC

pith:2019:ZCBURDMCULGSSPXMWDWNVK2ZE7

not attested not anchored not stored refs pending

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

Ching-Wei Ho, Ping Zhong

arxiv:1908.08150 v3 · 2019-08-22 · math.OA · math-ph · math.FA · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZCBURDMCULGSSPXMWDWNVK2ZE7}

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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

Strong Convergence of Multiplicative Brownian Motions on the General Linear Group

Receipt and verification

First computed	2026-07-05T03:18:23.490130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c883488d82a2cd293eecb0ecdaab5927c3c3b45f3e25ee3e1ffc0c2fa6019f5d

Aliases

arxiv: 1908.08150 · arxiv_version: 1908.08150v3 · doi: 10.48550/arxiv.1908.08150 · pith_short_12: ZCBURDMCULGS · pith_short_16: ZCBURDMCULGSSPXM · pith_short_8: ZCBURDMC

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/ZCBURDMCULGSSPXMWDWNVK2ZE7 \
  | 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: c883488d82a2cd293eecb0ecdaab5927c3c3b45f3e25ee3e1ffc0c2fa6019f5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99533dbd4a6dc05c3e82e32f8ab79128d78136a73b93409526b5dcbf8186109c",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-08-22T00:14:58Z",
    "title_canon_sha256": "b9ee5933157cd3e801160bf374e50a94bca725e810a7bed6db48b619c4966b44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08150",
    "kind": "arxiv",
    "version": 3
  }
}