Pith Number

pith:ESSONI5I

pith:2016:ESSONI5IFCVWA22ZYTDWDZPYSA

not attested not anchored not stored refs pending

Strong approximations for the $p$-fold integrated empirical process with applications to statistical tests

Aim\'e Lachal, Salim Bouzebda, Sergio Alvarez-Andrade

arxiv:1611.04513 v2 · 2016-11-10 · 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{ESSONI5IFCVWA22ZYTDWDZPYSA}

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	2026-05-17T23:51:20.234610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24a4e6a3a828ab606b59c4c761e5f89016a65a65fe2de0a96a79561edfbc735a

Aliases

arxiv: 1611.04513 · arxiv_version: 1611.04513v2 · doi: 10.48550/arxiv.1611.04513 · pith_short_12: ESSONI5IFCVW · pith_short_16: ESSONI5IFCVWA22Z · pith_short_8: ESSONI5I

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/ESSONI5IFCVWA22ZYTDWDZPYSA \
  | 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: 24a4e6a3a828ab606b59c4c761e5f89016a65a65fe2de0a96a79561edfbc735a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0c7cd2bf7981c5554671c90a5ba6ed7ea3a3fefb4922460a2a18d73c6a8496c",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2016-11-10T06:54:50Z",
    "title_canon_sha256": "e5e783c678e8876174dedca3e47901a8474610530182b0f214dfa77dae0ffd9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04513",
    "kind": "arxiv",
    "version": 2
  }
}