Pith Number

pith:XAHMFUIQ

pith:2009:XAHMFUIQY45WYX56ZSXPDO5KD3

not attested not anchored not stored refs pending

Buffon's needle landing near Besicovitch irregular self-similar sets

Alexander Volberg, Matt Bond

arxiv:0912.5111 v3 · 2009-12-27 · math.AP · math.CA · 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{XAHMFUIQY45WYX56ZSXPDO5KD3}

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	2026-05-18T04:32:00.050267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b80ec2d110c73b6c5fbeccaef1bbaa1ec019ddf77e7dbfe6c6564dcb76ebe233

Aliases

arxiv: 0912.5111 · arxiv_version: 0912.5111v3 · doi: 10.48550/arxiv.0912.5111 · pith_short_12: XAHMFUIQY45W · pith_short_16: XAHMFUIQY45WYX56 · pith_short_8: XAHMFUIQ

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/XAHMFUIQY45WYX56ZSXPDO5KD3 \
  | 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: b80ec2d110c73b6c5fbeccaef1bbaa1ec019ddf77e7dbfe6c6564dcb76ebe233

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3c63a985f5792f5e23a9494ad649bee86d003792de1236cd90e518cc8e088a0",
    "cross_cats_sorted": [
      "math.CA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-12-27T22:17:44Z",
    "title_canon_sha256": "881903ed5fb8826bdc82050848303f77ee700e1af692853d16341caf28b1db08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.5111",
    "kind": "arxiv",
    "version": 3
  }
}