Pith Number

pith:VAZWGHXM

pith:2009:VAZWGHXMMK5PEAJHQI45QSRF52

not attested not anchored not stored refs pending

Rational numbers with purely periodic $\beta$-expansion

Anne Siegel (INRIA - IRISA), Boris Adamczewski (ICJ), Christiane Frougny (LIAFA), Wolfgang Steiner (LIAFA)

arxiv:0907.0206 v2 · 2009-07-01 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VAZWGHXMMK5PEAJHQI45QSRF52}

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	2026-05-18T02:58:03.009417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a833631eec62baf201278239d84a25ee846658d656cc5ecdafc864c91e0b98f3

Aliases

arxiv: 0907.0206 · arxiv_version: 0907.0206v2 · doi: 10.48550/arxiv.0907.0206 · pith_short_12: VAZWGHXMMK5P · pith_short_16: VAZWGHXMMK5PEAJH · pith_short_8: VAZWGHXM

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/VAZWGHXMMK5PEAJHQI45QSRF52 \
  | 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: a833631eec62baf201278239d84a25ee846658d656cc5ecdafc864c91e0b98f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a46bc732ef014c8b0fdf15e001dac1a1d946115aaa650efab42495bd30c42270",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-07-01T17:22:06Z",
    "title_canon_sha256": "713ecb5fe37b86cd5931ddcab86b63c2e6bc1182cc3910cb1a8c051ab94a0e0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0206",
    "kind": "arxiv",
    "version": 2
  }
}