Pith Number

pith:OALZLWN3

pith:2019:OALZLWN3FFT36BTVZV52EAUVLI

not attested not anchored not stored refs pending

Deep Network Approximation Characterized by Number of Neurons

Haizhao Yang, Shijun Zhang, Zuowei Shen

arxiv:1906.05497 v5 · 2019-06-13 · math.NA · cs.LG · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OALZLWN3FFT36BTVZV52EAUVLI}

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

4 papers in Pith

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations

Learning Sparse Compositional Functions with Norm-Constrained Neural Networks

Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations

Receipt and verification

First computed	2026-07-05T02:06:47.472675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

701795d9bb2967bf0675cd7ba202955a16285223e9d757f186c40c7fa851b72a

Aliases

arxiv: 1906.05497 · arxiv_version: 1906.05497v5 · doi: 10.48550/arxiv.1906.05497 · pith_short_12: OALZLWN3FFT3 · pith_short_16: OALZLWN3FFT36BTV · pith_short_8: OALZLWN3

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/OALZLWN3FFT36BTVZV52EAUVLI \
  | 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: 701795d9bb2967bf0675cd7ba202955a16285223e9d757f186c40c7fa851b72a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4259ff4e331f04e755dc54a9c46c7b3ccd26673a3cabfcb1f746cbc46ee6a588",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-06-13T06:15:15Z",
    "title_canon_sha256": "0b918275268b551fff572ce8f87f9250740adcb1794e96c630a25dd4961e6519"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.05497",
    "kind": "arxiv",
    "version": 5
  }
}