Pith Number

pith:L6EZ4CD2

pith:2015:L6EZ4CD2NOZMTZZUTPAHNX4UIH

not attested not anchored not stored refs pending

Applications of Realizations (aka Linearizations) to Free Probability

J. William Helton, Roland Speicher, Tobias Mai

arxiv:1511.05330 v2 · 2015-11-17 · math.OA · math.FA · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L6EZ4CD2NOZMTZZUTPAHNX4UIH}

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	2026-05-18T00:34:05.340869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f899e087a6bb2c9e7349bc076df9441f2aa111af80805e9239de83144d6c84d

Aliases

arxiv: 1511.05330 · arxiv_version: 1511.05330v2 · doi: 10.48550/arxiv.1511.05330 · pith_short_12: L6EZ4CD2NOZM · pith_short_16: L6EZ4CD2NOZMTZZU · pith_short_8: L6EZ4CD2

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/L6EZ4CD2NOZMTZZUTPAHNX4UIH \
  | 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: 5f899e087a6bb2c9e7349bc076df9441f2aa111af80805e9239de83144d6c84d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f1c8f51423ef16f960fc69c6d321c8d03e6e4f93ce652d47884c431ce05adfe",
    "cross_cats_sorted": [
      "math.FA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-11-17T10:11:29Z",
    "title_canon_sha256": "64ffb335c90ce4ef99e0e1b942c32db40a87e5578b17738f97fac563fdd30e6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.05330",
    "kind": "arxiv",
    "version": 2
  }
}