Pith Number

pith:VXUG2K3O

pith:2019:VXUG2K3OHXJ6UDPQMGVV4YCYO5

not attested not anchored not stored refs pending

A mean-field limit for certain deep neural networks

Daniel Yukimura, Dyego Ara\'ujo, Roberto I. Oliveira

arxiv:1906.00193 v1 · 2019-06-01 · math.ST · cond-mat.dis-nn · math.PR · 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{VXUG2K3OHXJ6UDPQMGVV4YCYO5}

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.

Cited by

1 paper in Pith

Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks

Receipt and verification

First computed	2026-05-17T23:44:27.842552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ade86d2b6e3dd3ea0df061ab5e6058775c6faefdc048c72c653481962d841a9f

Aliases

arxiv: 1906.00193 · arxiv_version: 1906.00193v1 · doi: 10.48550/arxiv.1906.00193 · pith_short_12: VXUG2K3OHXJ6 · pith_short_16: VXUG2K3OHXJ6UDPQ · pith_short_8: VXUG2K3O

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/VXUG2K3OHXJ6UDPQMGVV4YCYO5 \
  | 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: ade86d2b6e3dd3ea0df061ab5e6058775c6faefdc048c72c653481962d841a9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c019aacecb868d080d66c2ebb1805d3a5f02f6694fe2a93185b4a7e87b97afa",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2019-06-01T09:51:35Z",
    "title_canon_sha256": "339463bfa8589009ec0d12497a6864d76dd92605220a2f06304f9bd569ae51a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.00193",
    "kind": "arxiv",
    "version": 1
  }
}