Pith Number

pith:FUKMODIH

pith:2010:FUKMODIHKIORQDYUDYAI6N23DC

not attested not anchored not stored refs pending

Transformations generating negative $\beta$-expansions

Charlene Kalle, Karma Dajani

arxiv:1008.4289 v1 · 2010-08-25 · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FUKMODIHKIORQDYUDYAI6N23DC}

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	2026-05-18T04:41:53.247005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d14c70d07521d180f141e008f375b189c7d4bea6eb52f2647e59ed575604ec1

Aliases

arxiv: 1008.4289 · arxiv_version: 1008.4289v1 · doi: 10.48550/arxiv.1008.4289 · pith_short_12: FUKMODIHKIOR · pith_short_16: FUKMODIHKIORQDYU · pith_short_8: FUKMODIH

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/FUKMODIHKIORQDYUDYAI6N23DC \
  | 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: 2d14c70d07521d180f141e008f375b189c7d4bea6eb52f2647e59ed575604ec1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f42adc7fa69a28026f0fdf58ab98816d0075d18e2f09c868ab2051c63f891a2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-08-25T14:19:18Z",
    "title_canon_sha256": "138140a8a27e4e74fff6bb1eb7d921235bd8347b53b5710672e3ec4d54f9887e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4289",
    "kind": "arxiv",
    "version": 1
  }
}