Pith Number

pith:7PQU45XF

pith:2011:7PQU45XFEE62ZEIWJFDPBLZWSH

not attested not anchored not stored refs pending

Generalized Likelihood Ratio Statistics and Uncertainty Adjustments in Efficient Adaptive Design of Clinical Trials

Jay Bartroff, Tze Leung Lai

arxiv:1105.4667 v1 · 2011-05-24 · math.ST · 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{7PQU45XFEE62ZEIWJFDPBLZWSH}

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	2026-05-18T04:21:21.962216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbe14e76e5213dac91164946f0af3691dfb4ea1094c5dbf4cb827de91d6a47e0

Aliases

arxiv: 1105.4667 · arxiv_version: 1105.4667v1 · doi: 10.48550/arxiv.1105.4667 · pith_short_12: 7PQU45XFEE62 · pith_short_16: 7PQU45XFEE62ZEIW · pith_short_8: 7PQU45XF

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/7PQU45XFEE62ZEIWJFDPBLZWSH \
  | 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: fbe14e76e5213dac91164946f0af3691dfb4ea1094c5dbf4cb827de91d6a47e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "617e3baab158ba969938277356734428512eadca1d0ba5f9220a2ae50a53a501",
    "cross_cats_sorted": [
      "stat.ME",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2011-05-24T01:58:41Z",
    "title_canon_sha256": "a65339300ff307a2bfacad478296fc64ff2537412e28d9116a2b1d2a0d120c63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4667",
    "kind": "arxiv",
    "version": 1
  }
}