Pith Number

pith:NXD7F5YK

pith:2016:NXD7F5YKEM6VNKXTDRQI6QJPFX

not attested not anchored not stored refs pending

Beta-expansion and continued fraction expansion of real numbers

Bing Li, Lulu Fang, Min Wu

arxiv:1603.01081 v1 · 2016-03-03 · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NXD7F5YKEM6VNKXTDRQI6QJPFX}

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	2026-05-18T01:19:39.722919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6dc7f2f70a233d56aaf31c608f412f2ddcbcef22794e3cfbc01c1d61e71d8325

Aliases

arxiv: 1603.01081 · arxiv_version: 1603.01081v1 · doi: 10.48550/arxiv.1603.01081 · pith_short_12: NXD7F5YKEM6V · pith_short_16: NXD7F5YKEM6VNKXT · pith_short_8: NXD7F5YK

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/NXD7F5YKEM6VNKXTDRQI6QJPFX \
  | 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: 6dc7f2f70a233d56aaf31c608f412f2ddcbcef22794e3cfbc01c1d61e71d8325

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c0e68f3a62a00aaf655de4413a610b1f0477a1c8cfe0bae9fe3f25d82824aad",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-03-03T13:00:08Z",
    "title_canon_sha256": "c15a6cb4689ed8f2752b467cf37ca731d2fa519335f3aacd857105fddaee6c8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.01081",
    "kind": "arxiv",
    "version": 1
  }
}