Pith Number

pith:OQD3R5IQ

pith:2013:OQD3R5IQMQ2ZTLXXKCO4FS45BK

not attested not anchored not stored refs pending

Free Probability for Pairs of Faces I

Dan-Virgil Voiculescu

arxiv:1306.6082 v1 · 2013-06-25 · math.OA · 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{OQD3R5IQMQ2ZTLXXKCO4FS45BK}

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	2026-05-18T01:49:07.882515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7407b8f510643599aef7509dc2cb9d0aa1392c44952c4f4250d8d1bc742e431f

Aliases

arxiv: 1306.6082 · arxiv_version: 1306.6082v1 · doi: 10.48550/arxiv.1306.6082 · pith_short_12: OQD3R5IQMQ2Z · pith_short_16: OQD3R5IQMQ2ZTLXX · pith_short_8: OQD3R5IQ

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/OQD3R5IQMQ2ZTLXXKCO4FS45BK \
  | 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: 7407b8f510643599aef7509dc2cb9d0aa1392c44952c4f4250d8d1bc742e431f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b64c25e3bd2682da6a46ca8a8ce9c1b33b196ab0dbe4844c41b5ced02bec5e00",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-06-25T20:09:53Z",
    "title_canon_sha256": "d02bfa81202671bd4c06d59daf2985d9b5f12f54f5720524a15bef974f623c8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.6082",
    "kind": "arxiv",
    "version": 1
  }
}