Pith Number

pith:4AQC5FA5

pith:2007:4AQC5FA543TUGCOB4PVYG2R7WX

not attested not anchored not stored refs pending

On the statistics of the minimal solution of a linear Diophantine equation and uniform distribution of the real part of orbits in hyperbolic spaces

Morten S. Risager, Zeev Rudnick

arxiv:0707.3323 v4 · 2007-07-23 · 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{4AQC5FA543TUGCOB4PVYG2R7WX}

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	2026-05-18T04:09:15.517461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0202e941de6e74309c1e3eb836a3fb5d32235e652fc0407d71b354e8fb33e90

Aliases

arxiv: 0707.3323 · arxiv_version: 0707.3323v4 · doi: 10.48550/arxiv.0707.3323 · pith_short_12: 4AQC5FA543TU · pith_short_16: 4AQC5FA543TUGCOB · pith_short_8: 4AQC5FA5

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/4AQC5FA543TUGCOB4PVYG2R7WX \
  | 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: e0202e941de6e74309c1e3eb836a3fb5d32235e652fc0407d71b354e8fb33e90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5f0acf3ec1968f59b2eba4147fbc73ea35e01bf78b10cf81344607f8ddb5795",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-07-23T06:58:19Z",
    "title_canon_sha256": "bd3c43be2261a71782fbf7f04e5b889f111c2835291df2a79c791283ffb4a6dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.3323",
    "kind": "arxiv",
    "version": 4
  }
}