Pith Number

pith:Z5RJN6LN

pith:2015:Z5RJN6LN3MFP2O2HMBDWOVVY5V

not attested not anchored not stored refs pending

Free Probability for Pairs of Faces III: 2-Variables Bi-free Partial S- and T-Transforms

Dan-Virgil Voiculescu

arxiv:1504.03765 v2 · 2015-04-15 · 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{Z5RJN6LN3MFP2O2HMBDWOVVY5V}

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	2026-05-18T02:09:41.025500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf6296f96ddb0afd3b4760476756b8ed5a52f6343148858dd545be872da5d7f3

Aliases

arxiv: 1504.03765 · arxiv_version: 1504.03765v2 · doi: 10.48550/arxiv.1504.03765 · pith_short_12: Z5RJN6LN3MFP · pith_short_16: Z5RJN6LN3MFP2O2H · pith_short_8: Z5RJN6LN

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/Z5RJN6LN3MFP2O2HMBDWOVVY5V \
  | 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: cf6296f96ddb0afd3b4760476756b8ed5a52f6343148858dd545be872da5d7f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8c4631ab14fc29aef3421a06cae279ceb16c24c8254ea5e2b6c61fd26c5d3be",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-04-15T02:05:25Z",
    "title_canon_sha256": "9dee88c1f1a9991e9b80e648d98041550a5f4d5202a2b9c92f78df6e54da9459"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03765",
    "kind": "arxiv",
    "version": 2
  }
}