Pith Number

pith:U2MBJSMR

pith:2025:U2MBJSMRUSZUUFDQWYQ4GNMF42

not attested not anchored not stored refs pending

Besting Good--Turing: Optimality of Non-Parametric Maximum Likelihood for Distribution Estimation

Jonathan Niles-Weed, Yandi Shen, Yanjun Han, Yihong Wu

arxiv:2509.07355 v1 · 2025-09-09 · math.ST · cs.IT · math.IT · stat.ME · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U2MBJSMRUSZUUFDQWYQ4GNMF42}

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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.

Cited by

4 papers in Pith

NOVA: Fundamental Limits of Knowledge Discovery Through AI

Poisson Empirical Bayes via Gamma-Smoothed Nonparametric Maximum Likelihood

Adaptivity of the NPMLE to finitely discrete mixing distributions in Gaussian/Poisson mixtures

Receipt and verification

First computed	2026-07-05T12:07:20.182879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a69814c991a4b34a1470b621c33585e6a4124390d2317ebaadc7cad1284348ab

Aliases

arxiv: 2509.07355 · arxiv_version: 2509.07355v1 · doi: 10.48550/arxiv.2509.07355 · pith_short_12: U2MBJSMRUSZU · pith_short_16: U2MBJSMRUSZUUFDQ · pith_short_8: U2MBJSMR

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/U2MBJSMRUSZUUFDQWYQ4GNMF42 \
  | 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: a69814c991a4b34a1470b621c33585e6a4124390d2317ebaadc7cad1284348ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3de6b0bf7d39af49784372e66c441de45211dab20a178f382a45c47e2160bb5e",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "stat.ME",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2025-09-09T03:04:06Z",
    "title_canon_sha256": "9fa2c27f7b1c4a91f5dab72d16aabf1c99cfad33dddde54c3299ec1f73aaf895"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.07355",
    "kind": "arxiv",
    "version": 1
  }
}