Pith Number

pith:7MPDYKOJ

pith:2025:7MPDYKOJQ76YICJENCJ5LGGAOG

not attested not anchored not stored refs pending

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data

Anastasis Kratsios, Daniel Roy, Tin Sum Cheng

arxiv:2509.00924 v1 · 2025-08-31 · stat.ML · cs.LG · cs.NA · cs.NE · math.NA · 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{7MPDYKOJQ76YICJENCJ5LGGAOG}

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

Adaptivity Under Realizability Constraints: Comparing In-Context and Agentic Learning

Receipt and verification

First computed	2026-07-05T12:02:24.725788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb1e3c29c987fd8409246893d598c071a86f6d30192985e24711c1f73694a213

Aliases

arxiv: 2509.00924 · arxiv_version: 2509.00924v1 · doi: 10.48550/arxiv.2509.00924 · pith_short_12: 7MPDYKOJQ76Y · pith_short_16: 7MPDYKOJQ76YICJE · pith_short_8: 7MPDYKOJ

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/7MPDYKOJQ76YICJENCJ5LGGAOG \
  | 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: fb1e3c29c987fd8409246893d598c071a86f6d30192985e24711c1f73694a213

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1fce652a97325c44e95343874d1cf9d7df791cb739663de510b6d181b30aba24",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "cs.NE",
      "math.NA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2025-08-31T16:20:27Z",
    "title_canon_sha256": "7a310d708c03061762dcd9392906f1afef80758260db0ce6d8f5ac0d37bdc281"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.00924",
    "kind": "arxiv",
    "version": 1
  }
}