Pith Number

pith:6ASJZYF2

pith:2011:6ASJZYF223ZSP3C2BQ77FTH464

not attested not anchored not stored refs pending

An Analogue of Hin\u{c}in's Characterization of Infinite Divisibility for Operator-Valued Free Probability

John D. Williams

arxiv:1110.2691 v3 · 2011-10-12 · math.OA · math.FA · 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{6ASJZYF223ZSP3C2BQ77FTH464}

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.

Receipt and verification

First computed	2026-05-18T04:09:26.730829Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0249ce0bad6f327ec5a0c3ff2ccfcf72ba011790f470a4f5b846a5f1335f24c

Aliases

arxiv: 1110.2691 · arxiv_version: 1110.2691v3 · doi: 10.48550/arxiv.1110.2691 · pith_short_12: 6ASJZYF223ZS · pith_short_16: 6ASJZYF223ZSP3C2 · pith_short_8: 6ASJZYF2

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/6ASJZYF223ZSP3C2BQ77FTH464 \
  | 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: f0249ce0bad6f327ec5a0c3ff2ccfcf72ba011790f470a4f5b846a5f1335f24c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30369e85fafc83fb4c00f4a72cbad7435d4edc92372e7e8afc355a4a364e0082",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-10-12T16:26:57Z",
    "title_canon_sha256": "3e494ab47c9e51d815b24f636fb4f89d648e28f18e9ade9f6931275bef2dba2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2691",
    "kind": "arxiv",
    "version": 3
  }
}