Pith Number

pith:I4K57FAU

pith:2009:I4K57FAUI5DJBAUDDWJKDTEK6N

not attested not anchored not stored refs pending

Schmidt's game, fractals, and numbers normal to no base

Barak Weiss, Dmitry Kleinbock, Lior Fishman, Ryan Broderick, Yann Bugeaud

arxiv:0909.4251 v4 · 2009-09-23 · 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{I4K57FAUI5DJBAUDDWJKDTEK6N}

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	2026-05-18T00:05:20.097127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4715df941447469082831d92a1cc8af3573bd4b093b89158c7967d753bdb9da4

Aliases

arxiv: 0909.4251 · arxiv_version: 0909.4251v4 · doi: 10.48550/arxiv.0909.4251 · pith_short_12: I4K57FAUI5DJ · pith_short_16: I4K57FAUI5DJBAUD · pith_short_8: I4K57FAU

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/I4K57FAUI5DJBAUDDWJKDTEK6N \
  | 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: 4715df941447469082831d92a1cc8af3573bd4b093b89158c7967d753bdb9da4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6607daecdf5380eae881d7444550355d399b6ab28243bb28a7bc805e6e7d72f0",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-09-23T16:36:13Z",
    "title_canon_sha256": "e96549873f05498ac5364af75e7166f81f1521f3350b60072b102562738badf8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4251",
    "kind": "arxiv",
    "version": 4
  }
}