Pith Number

pith:5CMTKPWE

pith:2012:5CMTKPWEGAKF55VAPWAGLAK7ZM

not attested not anchored not stored refs pending

Independent Events in a Simple Random Experiment and the Meaning of Independence

Isaac M. Sonin

arxiv:1204.6731 v1 · 2012-04-30 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5CMTKPWEGAKF55VAPWAGLAK7ZM}

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	2026-05-18T03:56:43.991947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e899353ec430145ef6a07d8065815fcb2eb909e2417900f5bbf8c0fc0d352f9a

Aliases

arxiv: 1204.6731 · arxiv_version: 1204.6731v1 · doi: 10.48550/arxiv.1204.6731 · pith_short_12: 5CMTKPWEGAKF · pith_short_16: 5CMTKPWEGAKF55VA · pith_short_8: 5CMTKPWE

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/5CMTKPWEGAKF55VAPWAGLAK7ZM \
  | 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: e899353ec430145ef6a07d8065815fcb2eb909e2417900f5bbf8c0fc0d352f9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5713ef12ac517e444561af7104bf2b6bfd5b0e5082ec148873d594fe19b9d2dc",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-04-30T19:23:10Z",
    "title_canon_sha256": "26307134a243cc2b74d990996f7aca6aede5f0b09166f0c54f4a0808e5979fff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.6731",
    "kind": "arxiv",
    "version": 1
  }
}