Pith Number

pith:2FCAW5WB

pith:2009:2FCAW5WB3HHTZA47PXIARUOBHM

not attested not anchored not stored refs pending

Beta-expansions, natural extensions and multiple tilings associated with Pisot units

Charlene Kalle, Wolfgang Steiner (LIAFA)

arxiv:0907.2676 v3 · 2009-07-15 · 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{2FCAW5WB3HHTZA47PXIARUOBHM}

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	2026-05-18T04:02:01.157027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1440b76c1d9cf3c839f7dd008d1c13b0d46e1b9b1395fca171019a89c7f2893

Aliases

arxiv: 0907.2676 · arxiv_version: 0907.2676v3 · doi: 10.48550/arxiv.0907.2676 · pith_short_12: 2FCAW5WB3HHT · pith_short_16: 2FCAW5WB3HHTZA47 · pith_short_8: 2FCAW5WB

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/2FCAW5WB3HHTZA47PXIARUOBHM \
  | 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: d1440b76c1d9cf3c839f7dd008d1c13b0d46e1b9b1395fca171019a89c7f2893

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e727737c86b829399fab23290b4867e9e69b635c7e86155d99ffb134d72d49f1",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-07-15T18:17:04Z",
    "title_canon_sha256": "b9828cfd420c0b5d98448febed2e99c6c4eecaa53c1c643ef6037fcbba8b4901"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2676",
    "kind": "arxiv",
    "version": 3
  }
}