Pith Number

pith:KNOMUFW4

pith:2020:KNOMUFW4I6M2U7QSWRCK7PAHHD

not attested not anchored not stored refs pending

An overview on deep learning-based approximation methods for partial differential equations

Arnulf Jentzen, Benno Kuckuck, Christian Beck, Martin Hutzenthaler

arxiv:2012.12348 v3 · 2020-12-22 · math.NA · cs.LG · cs.NA

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\usepackage{pith}
\pithnumber{KNOMUFW4I6M2U7QSWRCK7PAHHD}

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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

3 papers in Pith

Random Neural Network Expressivity for Non-Linear Partial Differential Equations

Deep neural network approximation theory for high-dimensional functions

Stochastic Transition-Map Distillation for Fast Probabilistic Inference

Receipt and verification

First computed	2026-07-05T05:40:03.701887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

535cca16dc4799aa7e12b444afbc0738f40f2b24e3eb9e44cecf7a6044322bb0

Aliases

arxiv: 2012.12348 · arxiv_version: 2012.12348v3 · doi: 10.48550/arxiv.2012.12348 · pith_short_12: KNOMUFW4I6M2 · pith_short_16: KNOMUFW4I6M2U7QS · pith_short_8: KNOMUFW4

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/KNOMUFW4I6M2U7QSWRCK7PAHHD \
  | 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: 535cca16dc4799aa7e12b444afbc0738f40f2b24e3eb9e44cecf7a6044322bb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ca0d9dc4ec361cf9c51d04341ba35e56641674411d17e9f4f81af2941fee7c8",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2020-12-22T20:48:20Z",
    "title_canon_sha256": "4bbb8aa375ab849c59d50dc63f195b60389ae6a03cae04ba2669deb3909af6b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.12348",
    "kind": "arxiv",
    "version": 3
  }
}