Pith Number

pith:IHH7BNAB

pith:2024:IHH7BNABEX2IBWCZJF46356SBR

not attested not anchored not stored refs pending

Approximation Rates in Fr\'echet Metrics: Barron Spaces, Paley-Wiener Spaces, and Fourier Multipliers

Ahmed Abdeljawad, Thomas Dittrich

arxiv:2501.04023 v2 · 2024-12-27 · math.NA · cs.IT · cs.LG · cs.NA · math.IT · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IHH7BNABEX2IBWCZJF46356SBR}

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	2026-07-05T10:00:46.127812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41cff0b40125f480d8594979edf7d20c5ddc468ce012da9403332751be94074a

Aliases

arxiv: 2501.04023 · arxiv_version: 2501.04023v2 · doi: 10.48550/arxiv.2501.04023 · pith_short_12: IHH7BNABEX2I · pith_short_16: IHH7BNABEX2IBWCZ · pith_short_8: IHH7BNAB

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/IHH7BNABEX2IBWCZJF46356SBR \
  | 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: 41cff0b40125f480d8594979edf7d20c5ddc468ce012da9403332751be94074a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b11ca1387c14af54c209cfa7ab2b09a7cf7c91c8478fc757d4c500b8c0793b5",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.LG",
      "cs.NA",
      "math.IT",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2024-12-27T20:16:04Z",
    "title_canon_sha256": "2a2d94a4432b72269c72991e64ada6915a71fd4f7ec7b2a49a737e9825129e14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.04023",
    "kind": "arxiv",
    "version": 2
  }
}