Pith Number

pith:7R3RX3O6

pith:2022:7R3RX3O6VXN47JGAB4O3FG7ZAT

not attested not anchored not stored refs pending

The Brown measure of a sum of two free random variables, one of which is triangular elliptic

Ping Zhong, Serban Belinschi, Zhi Yin

arxiv:2209.11823 v3 · 2022-09-23 · 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{7R3RX3O6VXN47JGAB4O3FG7ZAT}

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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

Quaternionic Green's Function and the Brown Measure of Atomic Operators

Receipt and verification

First computed	2026-07-05T07:45:25.453713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc771beddeaddbcfa4c00f1db29bf904cb11e0606b98db49eb1bbc7a298ff530

Aliases

arxiv: 2209.11823 · arxiv_version: 2209.11823v3 · doi: 10.48550/arxiv.2209.11823 · pith_short_12: 7R3RX3O6VXN4 · pith_short_16: 7R3RX3O6VXN47JGA · pith_short_8: 7R3RX3O6

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/7R3RX3O6VXN47JGAB4O3FG7ZAT \
  | 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: fc771beddeaddbcfa4c00f1db29bf904cb11e0606b98db49eb1bbc7a298ff530

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0718225addb263fddc10a8cacc8422894ced24a64d64f9707c87bb8695f5a623",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2022-09-23T19:28:41Z",
    "title_canon_sha256": "93701658fc9303699e904f3bb3f8fa218e49400bed50c18cfbf17a96c1d85b1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.11823",
    "kind": "arxiv",
    "version": 3
  }
}