Pith Number

pith:F5JDUXME

pith:2017:F5JDUXMEEBCR2MTNOPZPZ2WL4E

not attested not anchored not stored refs pending

Detecting independence of random vectors: generalized distance covariance and Gaussian covariance

Bj\"orn B\"ottcher, Martin Keller-Ressel, Ren\'e L. Schilling

arxiv:1711.07778 v3 · 2017-11-21 · math.PR · 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{F5JDUXMEEBCR2MTNOPZPZ2WL4E}

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	2026-05-18T00:02:35.969231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f523a5d8420451d326d73f2fceacbe107410f473ca9ba58a78496f8e850f74c

Aliases

arxiv: 1711.07778 · arxiv_version: 1711.07778v3 · doi: 10.48550/arxiv.1711.07778 · pith_short_12: F5JDUXMEEBCR · pith_short_16: F5JDUXMEEBCR2MTN · pith_short_8: F5JDUXME

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/F5JDUXMEEBCR2MTNOPZPZ2WL4E \
  | 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: 2f523a5d8420451d326d73f2fceacbe107410f473ca9ba58a78496f8e850f74c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81cc951e1db084ecdd8c6fb59ebd02e3c010426e3677002e5b0d82cf73e3e47a",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-11-21T13:38:26Z",
    "title_canon_sha256": "52cb39868e0371a0aef9120b5598d3afc4640d437e4dd925b30d49d6103ba61d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.07778",
    "kind": "arxiv",
    "version": 3
  }
}