Pith Number

pith:243DKKV2

pith:2021:243DKKV2NV2HJYRZ5GZEMJJIA2

not attested not anchored not stored refs pending

Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networks

Yizhe Zhu, Zhichao Wang

arxiv:2109.09304 v3 · 2021-09-20 · math.ST · cs.LG · math.PR · stat.ML · 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{243DKKV2NV2HJYRZ5GZEMJJIA2}

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	2026-07-05T06:00:54.552356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d736352aba6d7474e239e9b24625280693dbc6a07baa43eb70510e392e1cffb1

Aliases

arxiv: 2109.09304 · arxiv_version: 2109.09304v3 · doi: 10.48550/arxiv.2109.09304 · pith_short_12: 243DKKV2NV2H · pith_short_16: 243DKKV2NV2HJYRZ · pith_short_8: 243DKKV2

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/243DKKV2NV2HJYRZ5GZEMJJIA2 \
  | 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: d736352aba6d7474e239e9b24625280693dbc6a07baa43eb70510e392e1cffb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b99bf2747d0946aeed65938bf4c87228ffdf7a0963ad81fd758162ff382c1b39",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2021-09-20T05:25:52Z",
    "title_canon_sha256": "f93ad7716f1f689c8e5ebcedb1ea4fa9bc15b3d1c6e2bb56bb2e0f1293103a8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.09304",
    "kind": "arxiv",
    "version": 3
  }
}