Pith Number

pith:T2AQTJAY

pith:2026:T2AQTJAY3E57XU5KLMZPGIIDSV

not attested not anchored not stored refs pending

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks

Sumio Watanabe

arxiv:2607.23397 v1 · 2026-07-26 · cs.LG · math.ST · 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{T2AQTJAY3E57XU5KLMZPGIIDSV}

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	2026-07-28T01:22:50.598850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e8109a418d93bfbd3aa5b32f3210395665cf69c6323ffa37f0d8567dfd089e8

Aliases

arxiv: 2607.23397 · arxiv_version: 2607.23397v1 · doi: 10.48550/arxiv.2607.23397 · pith_short_12: T2AQTJAY3E57 · pith_short_16: T2AQTJAY3E57XU5K · pith_short_8: T2AQTJAY

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/T2AQTJAY3E57XU5KLMZPGIIDSV \
  | 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: 9e8109a418d93bfbd3aa5b32f3210395665cf69c6323ffa37f0d8567dfd089e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4e537a8993afddd1f17df01a4f345158e44111e2edfd54c461c1807d2d63d77",
    "cross_cats_sorted": [
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-26T00:11:54Z",
    "title_canon_sha256": "8c2d5c1ec21fc4d15d789d64c2658d0782ff2f1bb146eb81ea3d8cf5f93ed919"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23397",
    "kind": "arxiv",
    "version": 1
  }
}