Pith Number

pith:J6FXDWIG

pith:2021:J6FXDWIGFCWXJMBTZ5LPYNWDDJ

not attested not anchored not stored refs pending

Brown measure of the sum of an elliptic operator and a free random variable in a finite von Neumann algebra

Ping Zhong

arxiv:2108.09844 v5 · 2021-08-22 · math.OA · math-ph · 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{J6FXDWIGFCWXJMBTZ5LPYNWDDJ}

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

2 papers in Pith

Eigenvalues, eigenvector-overlaps, and regularized Fuglede-Kadison determinant of the non-Hermitian matrix-valued Brownian motion

Brown measures of deformed $L^\infty$-valued circular elements

Receipt and verification

First computed	2026-07-05T11:58:15.297447Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f8b71d90628ad74b033cf56fc36c31a6e20dee2456ce95d058f9d041e5450b8

Aliases

arxiv: 2108.09844 · arxiv_version: 2108.09844v5 · doi: 10.48550/arxiv.2108.09844 · pith_short_12: J6FXDWIGFCWX · pith_short_16: J6FXDWIGFCWXJMBT · pith_short_8: J6FXDWIG

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/J6FXDWIGFCWXJMBTZ5LPYNWDDJ \
  | 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: 4f8b71d90628ad74b033cf56fc36c31a6e20dee2456ce95d058f9d041e5450b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c2490e137bd64450df2ecb5d07ce9e58deeacaec38e492914f6381335871570",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2021-08-22T21:10:11Z",
    "title_canon_sha256": "073081fdf13d75084692a5222fdb466f1b32079be10669c6744255571e989f34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.09844",
    "kind": "arxiv",
    "version": 5
  }
}