Pith Number

pith:C5YMIUD2

pith:2016:C5YMIUD2C64FNL73MGO2QJ4CRS

not attested not anchored not stored refs pending

Approximation orders of real numbers by $\beta$-expansions

Bing Li, Lulu Fang, Min Wu

arxiv:1603.08402 v2 · 2016-03-28 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C5YMIUD2C64FNL73MGO2QJ4CRS}

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	2026-05-18T01:10:39.818904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1770c4507a17b856affb619da827828cb12e30b43344399f6422b9802284e111

Aliases

arxiv: 1603.08402 · arxiv_version: 1603.08402v2 · doi: 10.48550/arxiv.1603.08402 · pith_short_12: C5YMIUD2C64F · pith_short_16: C5YMIUD2C64FNL73 · pith_short_8: C5YMIUD2

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/C5YMIUD2C64FNL73MGO2QJ4CRS \
  | 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: 1770c4507a17b856affb619da827828cb12e30b43344399f6422b9802284e111

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84168521152cffb955b8305162c823735a2dabc5cc6e5281207a4705fbec0523",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-03-28T15:33:52Z",
    "title_canon_sha256": "f3449da40961ec0b12f27cc54c3ed7b4f6a906164f913a43a3ef3fe856e473db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08402",
    "kind": "arxiv",
    "version": 2
  }
}