Pith Number

pith:OM5RBP4R

pith:2018:OM5RBP4RV64TWEKS7MK5ZGAKL5

not attested not anchored not stored refs pending

A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

Arnulf Jentzen, Fabian Hornung, Philippe von Wurstemberger, Philipp Grohs

arxiv:1809.02362 v3 · 2018-09-07 · math.NA · cs.LG · cs.NA · math.PR · q-fin.MF

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\usepackage{pith}
\pithnumber{OM5RBP4RV64TWEKS7MK5ZGAKL5}

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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	2026-07-05T06:36:17.742910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

733b10bf91afb93b1152fb15dc980a5f61a35d6a37b7ff7967f67109231eddab

Aliases

arxiv: 1809.02362 · arxiv_version: 1809.02362v3 · doi: 10.48550/arxiv.1809.02362 · pith_short_12: OM5RBP4RV64T · pith_short_16: OM5RBP4RV64TWEKS · pith_short_8: OM5RBP4R

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/OM5RBP4RV64TWEKS7MK5ZGAKL5 \
  | 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: 733b10bf91afb93b1152fb15dc980a5f61a35d6a37b7ff7967f67109231eddab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1017fd758d250546d2a6ba9c2c783d688cf425b262e6cc5d560b4ab4f6fc0ea9",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.PR",
      "q-fin.MF"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2018-09-07T09:03:55Z",
    "title_canon_sha256": "be6ace2fec49742819e74c5b22ca62070c411a863d37b2f29ac48a3726e79dfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.02362",
    "kind": "arxiv",
    "version": 3
  }
}