Pith Number

pith:VIPYQCQH

pith:2014:VIPYQCQHEU7BSSF4HYJJOZISWZ

not attested not anchored not stored refs pending

Beta-expansions of rational numbers in quadratic Pisot bases

Tom\'a\v{s} Hejda, Wolfgang Steiner

arxiv:1411.2419 v1 · 2014-11-10 · math.DS · cs.DM · math.CO · 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{VIPYQCQHEU7BSSF4HYJJOZISWZ}

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	2026-05-18T00:21:05.403643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa1f880a07253e1948bc3e12976512b65ca8ddadaecdc931e9516763b7b92894

Aliases

arxiv: 1411.2419 · arxiv_version: 1411.2419v1 · doi: 10.48550/arxiv.1411.2419 · pith_short_12: VIPYQCQHEU7B · pith_short_16: VIPYQCQHEU7BSSF4 · pith_short_8: VIPYQCQH

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/VIPYQCQHEU7BSSF4HYJJOZISWZ \
  | 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: aa1f880a07253e1948bc3e12976512b65ca8ddadaecdc931e9516763b7b92894

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1640f1ebe3716bfdc291588ad5c7bdadc4a907e83d09e4f6ad3adc262ba1b263",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-11-10T13:30:20Z",
    "title_canon_sha256": "fa175be98891a3cc5f42c7a5ad7883b1fc2e2a324c78527a79874dbfda9a7e9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.2419",
    "kind": "arxiv",
    "version": 1
  }
}