Pith Number

pith:7YYHZK4C

pith:2026:7YYHZK4C6L646LC757M4LBV4DJ

not attested not anchored not stored refs pending

Two-Sample Inference for Gaussian-Smoothed Wasserstein Costs with Finite Moments

Jiaping Yang, Yunxin Zhang

The plug-in estimator for the Gaussian-smoothed Wasserstein cost converges at rates determined by the distributions' polynomial moments.

arxiv:2605.09084 v2 · 2026-05-09 · math.ST · stat.TH

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\usepackage{pith}
\pithnumber{7YYHZK4C6L646LC757M4LBV4DJ}

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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.

Claims

C1strongest claim

For fixed smoothing and finite polynomial moments M_{q_μ}(μ)<∞, M_{q_ν}(ν)<∞ with q_μ,q_ν>p, we establish upper bounds in probability of order ρ_{q_μ,p,d}(m)+ρ_{q_ν,p,d}(n) where ρ_{q,p,d}(N)=N^{-(q-p)/(q+d)} for p<q<d+2p, N^{-1/2} log N at q=d+2p, and N^{-1/2} for q>d+2p.

C2weakest assumption

The distributions μ and ν possess finite polynomial moments of order q_μ and q_ν strictly greater than p; the smoothing parameter σ is fixed and positive.

C3one line summary

Provides probabilistic upper bounds of order depending on moment orders and a central limit theorem for two-sample estimators of Gaussian-smoothed p-Wasserstein distances under finite moments.

Receipt and verification

First computed	2026-05-28T02:04:49.236325Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe307cab82f2fdcf2c5fefd9c586bc1a79883950b031e656a814d57248968178

Aliases

arxiv: 2605.09084 · arxiv_version: 2605.09084v2 · doi: 10.48550/arxiv.2605.09084 · pith_short_12: 7YYHZK4C6L64 · pith_short_16: 7YYHZK4C6L646LC7 · pith_short_8: 7YYHZK4C

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/7YYHZK4C6L646LC757M4LBV4DJ \
  | 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: fe307cab82f2fdcf2c5fefd9c586bc1a79883950b031e656a814d57248968178

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40e8a69cf89b3f9e437f84b99c138b3c90b92b0fd33f76f8da1dd303c8a6bde4",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-09T17:49:04Z",
    "title_canon_sha256": "ce1c88cdc383fb5ba0c677da8480f40bd486825f5e8948f010fdcd17db71f9d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09084",
    "kind": "arxiv",
    "version": 2
  }
}