Pith Number

pith:VEDVBIBB

pith:2017:VEDVBIBBWSPB4W3YKJDVHZNKL3

not attested not anchored not stored refs pending

Distribution of $\alpha n + \beta$ modulo 1 over integers free from large and small primes

Kam Hung Yau

arxiv:1711.06422 v5 · 2017-11-17 · 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{VEDVBIBBWSPB4W3YKJDVHZNKL3}

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	2026-05-17T23:47:16.165968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a90750a021b49e1e5b78524753e5aa5ec5bb082a164f9dad76748e9439fb4226

Aliases

arxiv: 1711.06422 · arxiv_version: 1711.06422v5 · doi: 10.48550/arxiv.1711.06422 · pith_short_12: VEDVBIBBWSPB · pith_short_16: VEDVBIBBWSPB4W3Y · pith_short_8: VEDVBIBB

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/VEDVBIBBWSPB4W3YKJDVHZNKL3 \
  | 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: a90750a021b49e1e5b78524753e5aa5ec5bb082a164f9dad76748e9439fb4226

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b52e0da450a802760ef7a34eb88ddf7509e690665692742f4f5feed376b10516",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-11-17T06:15:54Z",
    "title_canon_sha256": "f1b22fd90aa084754c9e63003dfed886c1edbe4106ca5a05a1a4a3a69ad9bdcc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.06422",
    "kind": "arxiv",
    "version": 5
  }
}