Pith Number

pith:7Q4LZYNB

pith:2012:7Q4LZYNBNYXHR3OBXC6OAOWXUM

not attested not anchored not stored refs pending

Counting Beta Expansions and the Absolute Continuity of Bernoulli Convolutions

Tom Kempton

arxiv:1203.5698 v1 · 2012-03-26 · math.DS · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7Q4LZYNBNYXHR3OBXC6OAOWXUM}

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	2026-05-18T03:59:14.411477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc38bce1a16e2e78edc1b8bce03ad7a33106170e98321af56b6ac342029f5fed

Aliases

arxiv: 1203.5698 · arxiv_version: 1203.5698v1 · doi: 10.48550/arxiv.1203.5698 · pith_short_12: 7Q4LZYNBNYXH · pith_short_16: 7Q4LZYNBNYXHR3OB · pith_short_8: 7Q4LZYNB

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/7Q4LZYNBNYXHR3OBXC6OAOWXUM \
  | 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: fc38bce1a16e2e78edc1b8bce03ad7a33106170e98321af56b6ac342029f5fed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b7f8853c9cc5692e406950397d4424b811e538211c139be19b8b9d8d29987a8",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-03-26T15:19:50Z",
    "title_canon_sha256": "af4133151348c6ebd3614143f7c193ca7dafd455423f1a07e4d4e2a46904c022"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5698",
    "kind": "arxiv",
    "version": 1
  }
}