Pith Number

pith:MBUUAYOK

pith:2016:MBUUAYOKS4ILHXGLTCT2TLONNF

not attested not anchored not stored refs pending

On the distribution of $\alpha p^{\gamma}+\beta$ modulo one

Alexander Dunn

arxiv:1609.03188 v6 · 2016-09-11 · 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{MBUUAYOKS4ILHXGLTCT2TLONNF}

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	2026-05-18T00:29:10.907195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60694061ca9710b3dccb98a7a9adcd694da0ec8f27d9a247314e48d499d656da

Aliases

arxiv: 1609.03188 · arxiv_version: 1609.03188v6 · doi: 10.48550/arxiv.1609.03188 · pith_short_12: MBUUAYOKS4IL · pith_short_16: MBUUAYOKS4ILHXGL · pith_short_8: MBUUAYOK

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/MBUUAYOKS4ILHXGLTCT2TLONNF \
  | 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: 60694061ca9710b3dccb98a7a9adcd694da0ec8f27d9a247314e48d499d656da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d635e25f842646af8b03d3e490c7a2b7fb0429cf33588e8e5ebe8a35459081e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-11T18:18:37Z",
    "title_canon_sha256": "315e7cb134ece3aa429941c9ac230f9e7f815c6bf64616bbd66de6279ddaff8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03188",
    "kind": "arxiv",
    "version": 6
  }
}