Pith Number

pith:RFQGRSBE

pith:2002:RFQGRSBERZ72DX6GJYJJKDBMSY

not attested not anchored not stored refs pending

What is Stochastic Independence?

Uwe Franz

arxiv:math/0206017 v1 · 2002-06-03 · math.QA · math.CT · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RFQGRSBERZ72DX6GJYJJKDBMSY}

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.

Cited by

1 paper in Pith

A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics

Receipt and verification

First computed	2026-07-05T02:33:40.516177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

896068c8248e7fa1dfc64e12950c2c960b546a9db02136b4100fe1f5d13e19a5

Aliases

arxiv: math/0206017 · arxiv_version: math/0206017v1 · doi: 10.48550/arxiv.math/0206017 · pith_short_12: RFQGRSBERZ72 · pith_short_16: RFQGRSBERZ72DX6G · pith_short_8: RFQGRSBE

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/RFQGRSBERZ72DX6GJYJJKDBMSY \
  | 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: 896068c8248e7fa1dfc64e12950c2c960b546a9db02136b4100fe1f5d13e19a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5243a4cb41eb8387f711f468d5e0d2214838821f93a158f288aa74b38677cda3",
    "cross_cats_sorted": [
      "math.CT",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2002-06-03T17:07:39Z",
    "title_canon_sha256": "39c1ed5e4bb56b0e6f8b878ca771068ccf6460524c62a0ece59e2fdfd5b51218"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0206017",
    "kind": "arxiv",
    "version": 1
  }
}