Pith Number

pith:XBFTDI67

pith:2020:XBFTDI67ZSILZH6GLVVBGG7XOZ

not attested not anchored not stored refs pending

Space-time deep neural network approximations for high-dimensional partial differential equations

Arnulf Jentzen, Diyora Salimova, Fabian Hornung

arxiv:2006.02199 v2 · 2020-06-03 · math.PR · cs.LG · cs.NA · math.AP · math.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{XBFTDI67ZSILZH6GLVVBGG7XOZ}

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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

2 papers in Pith

Deep neural network approximation theory for high-dimensional functions

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^

Receipt and verification

First computed	2026-07-05T08:26:08.438781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b84b31a3dfcc90bc9fc65d6a131bf77647be34a3e4030373e1837e95ec5bee80

Aliases

arxiv: 2006.02199 · arxiv_version: 2006.02199v2 · doi: 10.48550/arxiv.2006.02199 · pith_short_12: XBFTDI67ZSIL · pith_short_16: XBFTDI67ZSILZH6G · pith_short_8: XBFTDI67

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/XBFTDI67ZSILZH6GLVVBGG7XOZ \
  | 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: b84b31a3dfcc90bc9fc65d6a131bf77647be34a3e4030373e1837e95ec5bee80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbd75f44b6666dbac93172118854211c6a97fb70d0ed74d6e0d95794284ef315",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.AP",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-06-03T12:14:56Z",
    "title_canon_sha256": "1c5a2e3ae1ac0e3966ca038bf30e9d1bfb3a3707e9d3db824adfd6d588919cb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.02199",
    "kind": "arxiv",
    "version": 2
  }
}