Pith Number

pith:P3AFWOF3

pith:2026:P3AFWOF33XLPE2MVSOSGLKXTZ4

not attested not anchored not stored refs pending

Sharp Lower Bound on the Minimax Risk for Multinomial Uniformity Testing via a Conditional Central Limit Theorem

Alon Kipnis

arxiv:2607.05223 v1 · 2026-07-06 · math.ST · cs.IT · math.IT · 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{P3AFWOF33XLPE2MVSOSGLKXTZ4}

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	2026-07-07T03:19:20.127659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ec05b38bbddd6f2699593a465aaf3cf136cac0e790fc10057b3f0278908ea98

Aliases

arxiv: 2607.05223 · arxiv_version: 2607.05223v1 · doi: 10.48550/arxiv.2607.05223 · pith_short_12: P3AFWOF33XLP · pith_short_16: P3AFWOF33XLPE2MV · pith_short_8: P3AFWOF3

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/P3AFWOF33XLPE2MVSOSGLKXTZ4 \
  | 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: 7ec05b38bbddd6f2699593a465aaf3cf136cac0e790fc10057b3f0278908ea98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72caccf4fa16c718ae51418d7a181e760119c31de11dd7e9527e6bf3d3331bbf",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-07-06T15:37:38Z",
    "title_canon_sha256": "a3b93b695424d6fa62abae96eadd3cfc35bc099561b34bc6d486aa030ee6038e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05223",
    "kind": "arxiv",
    "version": 1
  }
}