Pith Number

pith:ZPKYLY4O

pith:2016:ZPKYLY4OXWAGJRNXRNAMEXY6F5

not attested not anchored not stored refs pending

Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables

Han Cheng Lie, T. J. Sullivan

arxiv:1608.03784 v2 · 2016-08-12 · 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{ZPKYLY4OXWAGJRNXRNAMEXY6F5}

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	2026-05-18T00:56:06.189881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbd585e38ebd8064c5b78b40c25f1e2f5b67c152a66c9491ae27b3fc3202109d

Aliases

arxiv: 1608.03784 · arxiv_version: 1608.03784v2 · doi: 10.48550/arxiv.1608.03784 · pith_short_12: ZPKYLY4OXWAG · pith_short_16: ZPKYLY4OXWAGJRNX · pith_short_8: ZPKYLY4O

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/ZPKYLY4OXWAGJRNXRNAMEXY6F5 \
  | 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: cbd585e38ebd8064c5b78b40c25f1e2f5b67c152a66c9491ae27b3fc3202109d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b305107186564ac8b55233d60fbd72d0b162a295aaa9b9defb48e46f1d26b313",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-08-12T13:12:13Z",
    "title_canon_sha256": "164ac38fe4e9ad27d205688ae30c6f8c6b4a0741c9add6c4c8807949c6410c04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.03784",
    "kind": "arxiv",
    "version": 2
  }
}