Pith Number

pith:ENNCSJ4C

pith:2026:ENNCSJ4C3M4IRZ32GYHJKYLD6N

not attested not anchored not stored refs pending

Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One

Qi Zhou, Xiao-Song Yang, Xuan Zhou

arxiv:2607.04597 v1 · 2026-07-06 · cs.LG · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ENNCSJ4C3M4IRZ32GYHJKYLD6N}

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	2026-07-07T02:19:26.760027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

235a292782db3888e77a360e956163f37a3106eb6ef1c030aabed2e8ed0675f0

Aliases

arxiv: 2607.04597 · arxiv_version: 2607.04597v1 · doi: 10.48550/arxiv.2607.04597 · pith_short_12: ENNCSJ4C3M4I · pith_short_16: ENNCSJ4C3M4IRZ32 · pith_short_8: ENNCSJ4C

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/ENNCSJ4C3M4IRZ32GYHJKYLD6N \
  | 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: 235a292782db3888e77a360e956163f37a3106eb6ef1c030aabed2e8ed0675f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b58732672f76d09409a5e938db8668b284e01cb5e337a68461a96e701cf31607",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-06T01:58:37Z",
    "title_canon_sha256": "7eafcbf012760b87ed7a5255965431533deb91e1fa60eae2711590d912a1aeea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04597",
    "kind": "arxiv",
    "version": 1
  }
}