Pith Number

pith:3UI4ZG3K

pith:2019:3UI4ZG3KWYOXFE3Q5RD5MA2DGN

not attested not anchored not stored refs pending

Approximation spaces of deep neural networks

DANTE), Felix Voigtlaender (KU), Gitta Kutyniok, Morten Nielsen, R\'emi Gribonval (PANAMA

arxiv:1905.01208 v4 · 2019-05-03 · math.FA · cs.NE · 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{3UI4ZG3KWYOXFE3Q5RD5MA2DGN}

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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 approximation theory for high-dimensional functions

Receipt and verification

First computed	2026-07-05T01:20:04.561288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd11cc9b6ab61d729370ec47d60343337cff9cbd01c01d6b0b83068f07baef23

Aliases

arxiv: 1905.01208 · arxiv_version: 1905.01208v4 · doi: 10.48550/arxiv.1905.01208 · pith_short_12: 3UI4ZG3KWYOX · pith_short_16: 3UI4ZG3KWYOXFE3Q · pith_short_8: 3UI4ZG3K

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/3UI4ZG3KWYOXFE3Q5RD5MA2DGN \
  | 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: dd11cc9b6ab61d729370ec47d60343337cff9cbd01c01d6b0b83068f07baef23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89b3b2d44569d5db91751e372b690e15a784a1acaee4daaf7d71b4e303949239",
    "cross_cats_sorted": [
      "cs.NE",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-05-03T14:43:23Z",
    "title_canon_sha256": "54c873835dfdc68d532aaa9a5f55bdfe1ef2949fbf6cedf29bf47f384cfc35f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.01208",
    "kind": "arxiv",
    "version": 4
  }
}