Pith Number

pith:S5QXPEDB

pith:2019:S5QXPEDBAPTLD2SM3PL3TWVVF3

not attested not anchored not stored refs pending

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

Arnulf Jentzen, Martin Hutzenthaler, Thomas Kruse, Tuan Anh Nguyen

arxiv:1901.10854 v2 · 2019-01-30 · math.NA · cs.NA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S5QXPEDBAPTLD2SM3PL3TWVVF3}

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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

Deep neural network approximations for Monte Carlo algorithms

Receipt and verification

First computed	2026-07-05T01:53:45.281084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

976177906103e6b1ea4cdbd7b9dab52ef3cb90dc72a5762615375f43f0a2a1f0

Aliases

arxiv: 1901.10854 · arxiv_version: 1901.10854v2 · doi: 10.48550/arxiv.1901.10854 · pith_short_12: S5QXPEDBAPTL · pith_short_16: S5QXPEDBAPTLD2SM · pith_short_8: S5QXPEDB

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/S5QXPEDBAPTLD2SM3PL3TWVVF3 \
  | 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: 976177906103e6b1ea4cdbd7b9dab52ef3cb90dc72a5762615375f43f0a2a1f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46c32a49d94f123104d9b7575942a002ac0657a760600c18229a52064ae8de01",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-01-30T14:37:35Z",
    "title_canon_sha256": "9330e63126368753b056de73187cb0c97e6e132f4e8c6e310a3aa4c928ea7d4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.10854",
    "kind": "arxiv",
    "version": 2
  }
}