Pith Number

pith:RAJT52UH

pith:2018:RAJT52UHONKZFNLA6UQLVEA3AR

not attested not anchored not stored refs pending

Diophantine approximation and run-length function on \beta-expansions

Lixuan Zheng

arxiv:1805.04744 v3 · 2018-05-12 · 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{RAJT52UHONKZFNLA6UQLVEA3AR}

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	2026-05-18T00:10:44.570269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88133eea87735592b560f520ba901b044763ced0206f067fc5f552a48b85e28a

Aliases

arxiv: 1805.04744 · arxiv_version: 1805.04744v3 · doi: 10.48550/arxiv.1805.04744 · pith_short_12: RAJT52UHONKZ · pith_short_16: RAJT52UHONKZFNLA · pith_short_8: RAJT52UH

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/RAJT52UHONKZFNLA6UQLVEA3AR \
  | 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: 88133eea87735592b560f520ba901b044763ced0206f067fc5f552a48b85e28a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "543bc5ec154509046e7ba34935cf6209914e365abf18a932a96702c9b407c8b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-05-12T15:58:49Z",
    "title_canon_sha256": "ed56cdbc0e2d2d4d0ae8f7076295d73f156f35eef5b55e7601c8fe73d444369c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.04744",
    "kind": "arxiv",
    "version": 3
  }
}