Pith Number

pith:B3QBWGGX

pith:2012:B3QBWGGX6KPLLTZSPV7MXQMKIP

not attested not anchored not stored refs pending

Three lectures on free probability

Jonathan Novak, Michael LaCroix

arxiv:1205.2097 v1 · 2012-05-09 · math.CO · math-ph · math.MP · 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{B3QBWGGX6KPLLTZSPV7MXQMKIP}

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	2026-05-18T03:55:57.052280Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ee01b18d7f29eb5cf327d7ecbc18a43df89e530d7c07a4091dff026e6ed7c7e

Aliases

arxiv: 1205.2097 · arxiv_version: 1205.2097v1 · doi: 10.48550/arxiv.1205.2097 · pith_short_12: B3QBWGGX6KPL · pith_short_16: B3QBWGGX6KPLLTZS · pith_short_8: B3QBWGGX

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/B3QBWGGX6KPLLTZSPV7MXQMKIP \
  | 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: 0ee01b18d7f29eb5cf327d7ecbc18a43df89e530d7c07a4091dff026e6ed7c7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d75254b93b0c3e79673a54cb9ec7aaa7aba5b006ce86a5f5e92e5e3961493b2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-09T20:11:25Z",
    "title_canon_sha256": "fe1801dd3afeaf72c0b9d201bb6a9c69931bcb6bdaa845aa2b82e2b263d2ac6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2097",
    "kind": "arxiv",
    "version": 1
  }
}