Pith Number

pith:VLZRW22Z

pith:2016:VLZRW22ZGK45AKHBOPGPZBOEJV

not attested not anchored not stored refs pending

Quasi-invariance of countable products of Cauchy measures under non-unitary dilations

Han Cheng Lie, T. J. Sullivan

arxiv:1611.10289 v3 · 2016-11-30 · 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{VLZRW22ZGK45AKHBOPGPZBOEJV}

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	2026-05-18T00:21:29.068967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaf31b6b5932b9d028e173ccfc85c44d6aedb6e93832a132ba046bd662a5ad22

Aliases

arxiv: 1611.10289 · arxiv_version: 1611.10289v3 · doi: 10.48550/arxiv.1611.10289 · pith_short_12: VLZRW22ZGK45 · pith_short_16: VLZRW22ZGK45AKHB · pith_short_8: VLZRW22Z

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/VLZRW22ZGK45AKHBOPGPZBOEJV \
  | 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: aaf31b6b5932b9d028e173ccfc85c44d6aedb6e93832a132ba046bd662a5ad22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50f0f73cf42556b8e63d018ab279339a8d23c1ef28f0ea7a7e275f615837b128",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-30T17:50:25Z",
    "title_canon_sha256": "d661dc00d787cab3d96c95c65398c1ba1c1843b86d1bf01f64e1da763f8c7a99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.10289",
    "kind": "arxiv",
    "version": 3
  }
}