Pith Number

pith:4VUBTDTK

pith:2007:4VUBTDTKTDPL73SVHDF7FH7HNR

not attested not anchored not stored refs pending

A probabilistic proof of Wallis's formula for pi

Steven J. Miller

arxiv:0709.2181 v2 · 2007-09-13 · math.NT · 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{4VUBTDTKTDPL73SVHDF7FH7HNR}

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	2026-05-18T04:35:57.585094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e568198e6a98debfee5538cbf29fe76c452a78a19f64909d8d5779432f1241a9

Aliases

arxiv: 0709.2181 · arxiv_version: 0709.2181v2 · doi: 10.48550/arxiv.0709.2181 · pith_short_12: 4VUBTDTKTDPL · pith_short_16: 4VUBTDTKTDPL73SV · pith_short_8: 4VUBTDTK

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/4VUBTDTKTDPL73SVHDF7FH7HNR \
  | 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: e568198e6a98debfee5538cbf29fe76c452a78a19f64909d8d5779432f1241a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fdfcdc69c19c44901c228b7b6159a430f85d6e56623a7c30b160c912ba944bd",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-09-13T23:01:28Z",
    "title_canon_sha256": "adf446d5d8c42a4194fafe755ddd33d0153488f62e6eefa3c7eda15c6e346806"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2181",
    "kind": "arxiv",
    "version": 2
  }
}