Pith Number

pith:4MSEISDF

pith:2012:4MSEISDFQ4H5DOF5HYLPEVVGAE

not attested not anchored not stored refs pending

On digit patterns in expansions of rational numbers with prime denominator

Igor E. Shparlinski (Department of computing), Wolfgang Steiner (LIAFA)

arxiv:1205.5673 v1 · 2012-05-25 · 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{4MSEISDFQ4H5DOF5HYLPEVVGAE}

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	2026-05-18T03:54:50.609686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e324444865870fd1b8bd3e16f256a6010b0cf8fba78b15ea3025c45883c57718

Aliases

arxiv: 1205.5673 · arxiv_version: 1205.5673v1 · doi: 10.48550/arxiv.1205.5673 · pith_short_12: 4MSEISDFQ4H5 · pith_short_16: 4MSEISDFQ4H5DOF5 · pith_short_8: 4MSEISDF

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/4MSEISDFQ4H5DOF5HYLPEVVGAE \
  | 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: e324444865870fd1b8bd3e16f256a6010b0cf8fba78b15ea3025c45883c57718

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "729c0cfc265fa675438f8b1b0497d3610e2f442229aa2117398e54983d4cf20b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-05-25T12:03:11Z",
    "title_canon_sha256": "c3c2e26042e5c9938e5a256eb16f31a66607113ac1dec54adb0946c28837e789"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5673",
    "kind": "arxiv",
    "version": 1
  }
}