Pith Number

pith:COQRF3FJ

pith:2017:COQRF3FJHE6IRNQAUO7L2REF72

not attested not anchored not stored refs pending

Efron's monotonicity property for measures on $\mathbb{R}^2$

Adrien Saumard, Jon A. Wellner

arxiv:1707.04472 v2 · 2017-07-14 · math.ST · math.PR · 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{COQRF3FJHE6IRNQAUO7L2REF72}

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	2026-05-18T00:27:30.306981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13a112eca9393c88b600a3bebd4485fe9402cb7099d7522aecc1bf4153d57d27

Aliases

arxiv: 1707.04472 · arxiv_version: 1707.04472v2 · doi: 10.48550/arxiv.1707.04472 · pith_short_12: COQRF3FJHE6I · pith_short_16: COQRF3FJHE6IRNQA · pith_short_8: COQRF3FJ

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/COQRF3FJHE6IRNQAUO7L2REF72 \
  | 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: 13a112eca9393c88b600a3bebd4485fe9402cb7099d7522aecc1bf4153d57d27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "025bf3a68d35c117857f972ce85255246b265f2202f222fcd0aaeed6df876844",
    "cross_cats_sorted": [
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2017-07-14T11:55:37Z",
    "title_canon_sha256": "2ea6e2e51e2091d59f7c9ae1e57f8c27faeb48cea25496c9018a3312c2684ca1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.04472",
    "kind": "arxiv",
    "version": 2
  }
}