Pith Number

pith:LXM2E4IC

pith:2015:LXM2E4IC3XGCGUQOTUUMLLCZXZ

not attested not anchored not stored refs pending

On uniform approximation to real numbers

Johannes Schleischitz, Yann Bugeaud

arxiv:1512.00780 v4 · 2015-12-02 · 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{LXM2E4IC3XGCGUQOTUUMLLCZXZ}

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	2026-05-18T00:53:24.585151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dd9a27102ddcc23520e9d28c5ac59be7c16c99376b1c965d0abb8a9e21c1f15

Aliases

arxiv: 1512.00780 · arxiv_version: 1512.00780v4 · doi: 10.48550/arxiv.1512.00780 · pith_short_12: LXM2E4IC3XGC · pith_short_16: LXM2E4IC3XGCGUQO · pith_short_8: LXM2E4IC

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/LXM2E4IC3XGCGUQOTUUMLLCZXZ \
  | 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: 5dd9a27102ddcc23520e9d28c5ac59be7c16c99376b1c965d0abb8a9e21c1f15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc5645b912a61207686fdd2221e7c24a144e0dd33f711e446a85adb4c25d0a99",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-02T17:30:54Z",
    "title_canon_sha256": "b210611eaf3d93216d9302deeadf76baf1564f6f9557c3e361e8b5346d993cf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00780",
    "kind": "arxiv",
    "version": 4
  }
}