Pith Number

pith:KKOZJKI3

pith:2018:KKOZJKI3EOIXXMGEIOOFDBQTV3

not attested not anchored not stored refs pending

A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients

Arnulf Jentzen, Diyora Salimova, Timo Welti

arxiv:1809.07321 v2 · 2018-09-19 · math.NA · cs.LG · cs.NA · math.AP · math.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KKOZJKI3EOIXXMGEIOOFDBQTV3}

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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

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs

Receipt and verification

First computed	2026-07-05T03:21:03.489739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

529d94a91b23917bb0c4439c518613aee304a753df3a111952647e917724536e

Aliases

arxiv: 1809.07321 · arxiv_version: 1809.07321v2 · doi: 10.48550/arxiv.1809.07321 · pith_short_12: KKOZJKI3EOIX · pith_short_16: KKOZJKI3EOIXXMGE · pith_short_8: KKOZJKI3

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/KKOZJKI3EOIXXMGEIOOFDBQTV3 \
  | 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: 529d94a91b23917bb0c4439c518613aee304a753df3a111952647e917724536e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ef2300249f646262f4312cb1e7df2c76ee58c92ce57869e457f4f565d63f747",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2018-09-19T17:56:40Z",
    "title_canon_sha256": "4ccbacc6788c2bbb2ec5d9771e622e0106b6313ce5f22213f0832571a1194a8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.07321",
    "kind": "arxiv",
    "version": 2
  }
}