Pith Number

pith:ODGYC6SY

pith:2009:ODGYC6SYFEX3EHC3ML4R55CYED

not attested not anchored not stored refs pending

Growth rate for beta-expansions

De-Jun Feng, Nikita Sidorov

arxiv:0902.0488 v4 · 2009-02-03 · 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{ODGYC6SYFEX3EHC3ML4R55CYED}

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	2026-05-18T04:19:52.221333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70cd817a58292fb21c5b62f91ef45820fb8e69ce86f3929007538879c68981dc

Aliases

arxiv: 0902.0488 · arxiv_version: 0902.0488v4 · doi: 10.48550/arxiv.0902.0488 · pith_short_12: ODGYC6SYFEX3 · pith_short_16: ODGYC6SYFEX3EHC3 · pith_short_8: ODGYC6SY

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/ODGYC6SYFEX3EHC3ML4R55CYED \
  | 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: 70cd817a58292fb21c5b62f91ef45820fb8e69ce86f3929007538879c68981dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01ed4ff9fe78e895a837d8633fb76ad85bf750bde4ede5f8a815c0f95f8a0fd6",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-02-03T12:25:46Z",
    "title_canon_sha256": "d129defa2b0dac00bd7ce74512c7312cf1efc41be871d90b8ebbc5d7d8c9b479"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.0488",
    "kind": "arxiv",
    "version": 4
  }
}