Pith Number

pith:FJKKCFCS

pith:2025:FJKKCFCSNCRNHBH6IWXO7OH42L

not attested not anchored not stored refs pending

Sharp uniform approximation for spectral Barron functions by deep neural networks

Hao Yu, Pingbing Ming, Yulei Liao

arxiv:2507.06789 v1 · 2025-07-09 · math.NA · cs.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{FJKKCFCSNCRNHBH6IWXO7OH42L}

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

Barron regularity of many particle Schr\"odinger eigenfunctions

Receipt and verification

First computed	2026-07-05T11:34:23.039764Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a54a1145268a2d384fe45aeefb8fcd2c62ad2ee71673e6fe22b0d255e81e241

Aliases

arxiv: 2507.06789 · arxiv_version: 2507.06789v1 · doi: 10.48550/arxiv.2507.06789 · pith_short_12: FJKKCFCSNCRN · pith_short_16: FJKKCFCSNCRNHBH6 · pith_short_8: FJKKCFCS

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/FJKKCFCSNCRNHBH6IWXO7OH42L \
  | 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: 2a54a1145268a2d384fe45aeefb8fcd2c62ad2ee71673e6fe22b0d255e81e241

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5610a2b6b34456efe67027df8d44d55f130c0a3cf549e62c7867a8249328310",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-07-09T12:27:07Z",
    "title_canon_sha256": "0acdd78d86b2cb4f73ad376d8958139bfaed4910babb1599b032e7240e8775ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06789",
    "kind": "arxiv",
    "version": 1
  }
}