Pith Number

pith:D6JF5U5V

pith:2021:D6JF5U5VWYSX7CAEAPE77AMCZV

not attested not anchored not stored refs pending

On the Minimum Attainable Risk in Permutation Invariant Problems

Asaf Weinstein

arxiv:2110.06250 v3 · 2021-10-12 · math.ST · 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{D6JF5U5VWYSX7CAEAPE77AMCZV}

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

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

Receipt and verification

First computed	2026-06-09T02:08:24.557370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f925ed3b5b6257f880403c9ff8182cd7e426f275fe985cf4ca345e657498c7b

Aliases

arxiv: 2110.06250 · arxiv_version: 2110.06250v3 · doi: 10.48550/arxiv.2110.06250 · pith_short_12: D6JF5U5VWYSX · pith_short_16: D6JF5U5VWYSX7CAE · pith_short_8: D6JF5U5V

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/D6JF5U5VWYSX7CAEAPE77AMCZV \
  | 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: 1f925ed3b5b6257f880403c9ff8182cd7e426f275fe985cf4ca345e657498c7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d809a6d4217d6a49101d0d86a0362d3c81b835d4793d580b814173c5e1f4eb71",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2021-10-12T18:04:48Z",
    "title_canon_sha256": "5c546f6990ad7fbe56014d255fe7d895889ff822b11f411e12394c07029122b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.06250",
    "kind": "arxiv",
    "version": 3
  }
}