Pith Number

pith:4GKQWZDP

pith:2015:4GKQWZDPREDSTYBAZO44DBDYVO

not attested not anchored not stored refs pending

Free Probability for Pairs of Faces IV: Bi-free Extremes in the Plane

Dan-Virgil Voiculescu

arxiv:1505.05020 v3 · 2015-05-19 · 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{4GKQWZDPREDSTYBAZO44DBDYVO}

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	2026-05-18T01:35:30.091389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1950b646f890729e020cbb9c18478ab811aa7757a022959d03f295325010ac7

Aliases

arxiv: 1505.05020 · arxiv_version: 1505.05020v3 · doi: 10.48550/arxiv.1505.05020 · pith_short_12: 4GKQWZDPREDS · pith_short_16: 4GKQWZDPREDSTYBA · pith_short_8: 4GKQWZDP

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/4GKQWZDPREDSTYBAZO44DBDYVO \
  | 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: e1950b646f890729e020cbb9c18478ab811aa7757a022959d03f295325010ac7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2596fbc0b93fc4dc253b319682f5d8ac9d57f8f7df48b06d330dd4702939ef97",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-05-19T14:42:59Z",
    "title_canon_sha256": "467233c64a0bcb38b333bf38ce5eeab2a4f214bdc2f019ae9da2e458460dd10b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05020",
    "kind": "arxiv",
    "version": 3
  }
}