Pith Number

pith:CFW7WZKN

pith:2014:CFW7WZKNAJ7WAJO6GLQODRWBNB

not attested not anchored not stored refs pending

A Simple Direct Proof of Billingsley's Theorem

Fred Kochman, Richard Arratia

arxiv:1401.1553 v1 · 2014-01-08 · 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{CFW7WZKNAJ7WAJO6GLQODRWBNB}

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	2026-05-18T03:02:58.656374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

116dfb654d027f6025de32e0e1c6c16876f397466f57d8d48a5079f29436b0bf

Aliases

arxiv: 1401.1553 · arxiv_version: 1401.1553v1 · doi: 10.48550/arxiv.1401.1553 · pith_short_12: CFW7WZKNAJ7W · pith_short_16: CFW7WZKNAJ7WAJO6 · pith_short_8: CFW7WZKN

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/CFW7WZKNAJ7WAJO6GLQODRWBNB \
  | 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: 116dfb654d027f6025de32e0e1c6c16876f397466f57d8d48a5079f29436b0bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e41e518c118f9860c0efcd5b4d1311fe01497db2e6c14b7fed5bc2166182f16",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-01-08T00:57:22Z",
    "title_canon_sha256": "d84b2f1093e6f178aa6be89570376274c76f26d40711ea877c740f20a64e7a13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.1553",
    "kind": "arxiv",
    "version": 1
  }
}