Pith Number

pith:4VNUMSH5

pith:2004:4VNUMSH5TMLIM3LSGMKH3JSTUV

not attested not anchored not stored refs pending

Product of random projections, Jacobi ensembles and universality problems arising from free probability

Benoit Collins

arxiv:math/0406560 v1 · 2004-06-28 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4VNUMSH5TMLIM3LSGMKH3JSTUV}

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	2026-07-04T14:49:26.988788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e55b4648fd9b16866d7233147da653a54a428ad9d65ea923b87adfc07200d98b

Aliases

arxiv: math/0406560 · arxiv_version: math/0406560v1 · doi: 10.48550/arxiv.math/0406560 · pith_short_12: 4VNUMSH5TMLI · pith_short_16: 4VNUMSH5TMLIM3LS · pith_short_8: 4VNUMSH5

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/4VNUMSH5TMLIM3LSGMKH3JSTUV \
  | 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: e55b4648fd9b16866d7233147da653a54a428ad9d65ea923b87adfc07200d98b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2466451e9ca418143e22133f4944823506904e78f3b0cec6be47d687b4c951e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-06-28T08:43:44Z",
    "title_canon_sha256": "75e64755cd0e64292f4d4d8f041beeb876fbc4d7421a698c649f445d72433f14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406560",
    "kind": "arxiv",
    "version": 1
  }
}