Pith Number

pith:CKIL56GK

pith:2025:CKIL56GKC3D3A3QVS6IPSFJCEG

not attested not anchored not stored refs pending

Supermartingales for One-Sided Tests: Sufficient Monotone Likelihood Ratios are Sufficient

Peter D. Gr\"unwald, Wouter M. Koolen

arxiv:2502.04208 v2 · 2025-02-06 · 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{CKIL56GKC3D3A3QVS6IPSFJCEG}

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	2026-07-05T10:10:49.728442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1290bef8ca16c7b06e159790f9152221810fce1fd3acb0c277c0fff4894d7ec7

Aliases

arxiv: 2502.04208 · arxiv_version: 2502.04208v2 · doi: 10.48550/arxiv.2502.04208 · pith_short_12: CKIL56GKC3D3 · pith_short_16: CKIL56GKC3D3A3QV · pith_short_8: CKIL56GK

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/CKIL56GKC3D3A3QVS6IPSFJCEG \
  | 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: 1290bef8ca16c7b06e159790f9152221810fce1fd3acb0c277c0fff4894d7ec7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5305c18f56f951131b40b49543511ebcf91618228b0e846ec91755243ab8b031",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2025-02-06T16:48:47Z",
    "title_canon_sha256": "06c2e89c4fd2a7250e45507c9a7bd43b676d7f4505824feb9e077e9090d62250"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.04208",
    "kind": "arxiv",
    "version": 2
  }
}