Pith Number

pith:IK4RHCLP

pith:2013:IK4RHCLPYTVYPJYI7J7M7D3GON

not attested not anchored not stored refs pending

Analytic Function Theory for Operator-Valued Free Probability

John D. Williams

arxiv:1309.0877 v3 · 2013-09-04 · 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{IK4RHCLPYTVYPJYI7J7M7D3GON}

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	2026-05-18T02:51:06.481864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42b913896fc4eb87a708fa7ecf8f66737d9fde4475f16a32bccbe9bb4b75a54d

Aliases

arxiv: 1309.0877 · arxiv_version: 1309.0877v3 · doi: 10.48550/arxiv.1309.0877 · pith_short_12: IK4RHCLPYTVY · pith_short_16: IK4RHCLPYTVYPJYI · pith_short_8: IK4RHCLP

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/IK4RHCLPYTVYPJYI7J7M7D3GON \
  | 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: 42b913896fc4eb87a708fa7ecf8f66737d9fde4475f16a32bccbe9bb4b75a54d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2f5e848e151c0b7469f8fe104a806060cfbc14ef9e298852d6f46cc6790c8b8",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-09-04T00:24:51Z",
    "title_canon_sha256": "b21594c6f7902f3a7ef3b71c9514b79a8e3a8985a0b42b01fdc788fa7d82e071"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0877",
    "kind": "arxiv",
    "version": 3
  }
}