Pith Number

pith:N4BJL7BN

pith:2019:N4BJL7BNWHFWWGIO46BBYI5JFL

not attested not anchored not stored refs pending

A Hydrodynamic Exercise in Free Probability: Setting up Free Euler Equations

Dan-Virgil Voiculescu

arxiv:1902.02442 v3 · 2019-02-07 · math.OA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N4BJL7BNWHFWWGIO46BBYI5JFL}

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	2026-05-17T23:47:53.748083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f0295fc2db1cb6b190ee7821c23a92ad36222aad31ac2e0566beac322b64f15

Aliases

arxiv: 1902.02442 · arxiv_version: 1902.02442v3 · doi: 10.48550/arxiv.1902.02442 · pith_short_12: N4BJL7BNWHFW · pith_short_16: N4BJL7BNWHFWWGIO · pith_short_8: N4BJL7BN

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/N4BJL7BNWHFWWGIO46BBYI5JFL \
  | 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: 6f0295fc2db1cb6b190ee7821c23a92ad36222aad31ac2e0566beac322b64f15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6484ba2c01b85bac530de2286e16feae14c783aaf7e5b5637c6d1c9cc1387df2",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-02-07T01:28:48Z",
    "title_canon_sha256": "da317d2843f7f7854a15e47e87cdb33bc04fe10b7527cd12c5c54659f901dfb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.02442",
    "kind": "arxiv",
    "version": 3
  }
}