Pith Number

pith:KZUAJWTP

pith:2026:KZUAJWTPCZYYTJIN3HCTVXFHYR

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Optimal Sampling for Kernel Quadrature on Unbounded Domains

Christian Robert (CEREMADE), Edoardo Bandoni (CEREMADE), Julien Stoehr (CEREMADE)

Constructs an n-dependent kernel-agnostic sampling distribution achieving minimax worst-case error rates for quadrature over smoothness classes on unbounded domains.

arxiv:2605.18134 v1 · 2026-05-18 · stat.CO · stat.ME

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\usepackage{pith}
\pithnumber{KZUAJWTPCZYYTJIN3HCTVXFHYR}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We construct an explicit, n-dependent sampling distribution that achieves minimax rates for worst-case error over smoothness classes without requiring knowledge of the kernel.

C2weakest assumption

The existence and explicit constructibility of an n-dependent sampling distribution whose worst-case error matches the minimax rate over the smoothness class, independent of the kernel, for the chosen unbounded measures (Gaussian, Student-t).

C3one line summary

Constructs an n-dependent kernel-agnostic sampling distribution achieving minimax worst-case error rates for quadrature over smoothness classes on unbounded domains.

Receipt and verification

First computed	2026-05-20T00:05:17.731213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

566804da6f167189a50dd9c53adca7c448fa3581c76c0bcf6f6226e46b4aca65

Aliases

arxiv: 2605.18134 · arxiv_version: 2605.18134v1 · doi: 10.48550/arxiv.2605.18134 · pith_short_12: KZUAJWTPCZYY · pith_short_16: KZUAJWTPCZYYTJIN · pith_short_8: KZUAJWTP

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/KZUAJWTPCZYYTJIN3HCTVXFHYR \
  | 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: 566804da6f167189a50dd9c53adca7c448fa3581c76c0bcf6f6226e46b4aca65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fbb3067bc341f5c9f72388e1ec394f429f3aaa3581868c47f20b285a5ab2257",
    "cross_cats_sorted": [
      "stat.ME"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.CO",
    "submitted_at": "2026-05-18T09:39:11Z",
    "title_canon_sha256": "4a9a40c8e64b7318eb1a64888a8ad5b0f4d2bcab23b55e5e817391918eabb878"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18134",
    "kind": "arxiv",
    "version": 1
  }
}