Pith Number

pith:GHCM4KWX

pith:2019:GHCM4KWXYTT7GO53MK5VZIH7YF

not attested not anchored not stored refs pending

Generalised multilevel Picard approximations

Arnulf Jentzen, Michael B. Giles, Timo Welti

arxiv:1911.03188 v1 · 2019-11-08 · math.NA · cs.NA · math.AP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GHCM4KWXYTT7GO53MK5VZIH7YF}

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

1 paper in Pith

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	2026-07-05T00:18:00.387032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31c4ce2ad7c4e7f33bbb62bb5ca0ffc15a714b30fcc2aa5c7f6ffb2d77ae8964

Aliases

arxiv: 1911.03188 · arxiv_version: 1911.03188v1 · doi: 10.48550/arxiv.1911.03188 · pith_short_12: GHCM4KWXYTT7 · pith_short_16: GHCM4KWXYTT7GO53 · pith_short_8: GHCM4KWX

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/GHCM4KWXYTT7GO53MK5VZIH7YF \
  | 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: 31c4ce2ad7c4e7f33bbb62bb5ca0ffc15a714b30fcc2aa5c7f6ffb2d77ae8964

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b8480735342ae243e590a1087ce44ab75d11cad469bac193b61d70f32b0eba9",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2019-11-08T11:18:27Z",
    "title_canon_sha256": "70ab0e1f59cd7f322c29c0776b25c6a0ed7969192c9a46aa2dc56f240c70cc40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.03188",
    "kind": "arxiv",
    "version": 1
  }
}