Pith Number

pith:KYEFXYKU

pith:2015:KYEFXYKUUJFCCT3ZHCGP33WFOO

not attested not anchored not stored refs pending

Entropic CLT and phase transition in high-dimensional Wishart matrices

S\'ebastien Bubeck, Shirshendu Ganguly

arxiv:1509.03258 v3 · 2015-09-10 · math.PR · cs.IT · math.FA · math.IT · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KYEFXYKUUJFCCT3ZHCGP33WFOO}

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	2026-05-18T00:08:24.239880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56085be154a24a214f79388cfdeec573a6434c9d85a6a8ea5fb4e0a1649d4512

Aliases

arxiv: 1509.03258 · arxiv_version: 1509.03258v3 · doi: 10.48550/arxiv.1509.03258 · pith_short_12: KYEFXYKUUJFC · pith_short_16: KYEFXYKUUJFCCT3Z · pith_short_8: KYEFXYKU

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/KYEFXYKUUJFCCT3ZHCGP33WFOO \
  | 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: 56085be154a24a214f79388cfdeec573a6434c9d85a6a8ea5fb4e0a1649d4512

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64a2f96e2d33d11bef15c959fdfd717f17b9ef8055fa9b57db7ea4f27a36e79f",
    "cross_cats_sorted": [
      "cs.IT",
      "math.FA",
      "math.IT",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-10T18:37:23Z",
    "title_canon_sha256": "28c4701e3e6fa668606d3acd58ee949bd1c57335fb2339b3a41435d231e2ea34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03258",
    "kind": "arxiv",
    "version": 3
  }
}