Pith Number

pith:XTICYKO2

pith:2013:XTICYKO2XXXEVYTZFPFAB5RKLG

not attested not anchored not stored refs pending

On digit frequencies in {\beta}-expansions

Andr\'e de Carvalho, Philip Boyland, Toby Hall

arxiv:1308.4437 v2 · 2013-08-20 · 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{XTICYKO2XXXEVYTZFPFAB5RKLG}

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	2026-05-18T02:43:54.281935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcd02c29dabdee4ae2792bca00f62a59ab134b8fa3ca7dcbc01ac99405a5da13

Aliases

arxiv: 1308.4437 · arxiv_version: 1308.4437v2 · doi: 10.48550/arxiv.1308.4437 · pith_short_12: XTICYKO2XXXE · pith_short_16: XTICYKO2XXXEVYTZ · pith_short_8: XTICYKO2

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/XTICYKO2XXXEVYTZFPFAB5RKLG \
  | 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: bcd02c29dabdee4ae2792bca00f62a59ab134b8fa3ca7dcbc01ac99405a5da13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e17dc9ebd5f30d4e1e9f25acc2ba5a0ded0b46db0257b0976e10100cf8a2cb9",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-08-20T21:29:00Z",
    "title_canon_sha256": "7a9111e493de201637bd31b2dc7689bfe48cb4c64c0ec8834af3e4ceb6e24029"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4437",
    "kind": "arxiv",
    "version": 2
  }
}