Pith Number

pith:JGHSJDDN

pith:2023:JGHSJDDNS7OON2JKXFO4TGR3PT

not attested not anchored not stored refs pending

Weighted variation spaces and approximation by shallow ReLU networks

Jonathan W. Siegel, Rahul Parhi, Robert D. Nowak, Ronald DeVore

arxiv:2307.15772 v2 · 2023-07-28 · stat.ML · cs.LG · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JGHSJDDNS7OON2JKXFO4TGR3PT}

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.

Receipt and verification

First computed	2026-07-05T09:38:48.157046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

498f248c6d97dce6e92ab95dc99a3b7cd3da31dcf7c071d19875fbd07a77fac4

Aliases

arxiv: 2307.15772 · arxiv_version: 2307.15772v2 · doi: 10.48550/arxiv.2307.15772 · pith_short_12: JGHSJDDNS7OO · pith_short_16: JGHSJDDNS7OON2JK · pith_short_8: JGHSJDDN

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/JGHSJDDNS7OON2JKXFO4TGR3PT \
  | 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: 498f248c6d97dce6e92ab95dc99a3b7cd3da31dcf7c071d19875fbd07a77fac4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a07612454e15242c254a6bc551e9f2279cc20877717ae7cea74d2659290239c4",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2023-07-28T19:14:42Z",
    "title_canon_sha256": "a69558f00a46ad12805429e73efba2b8b382ec0db3c983e920e00167780384ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2307.15772",
    "kind": "arxiv",
    "version": 2
  }
}