Pith Number

pith:6X4GRJ6W

pith:2013:6X4GRJ6WKCV3C2BPLEO6NAPQ3G

not attested not anchored not stored refs pending

A remark on solutions of the Pell equation

Jean Bourgain

arxiv:1311.5911 v1 · 2013-11-22 · 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{6X4GRJ6WKCV3C2BPLEO6NAPQ3G}

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	2026-05-18T03:06:21.130921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5f868a7d650abb1682f591de681f0d9af4747a9d70e59e7c698785e7a19cb83

Aliases

arxiv: 1311.5911 · arxiv_version: 1311.5911v1 · doi: 10.48550/arxiv.1311.5911 · pith_short_12: 6X4GRJ6WKCV3 · pith_short_16: 6X4GRJ6WKCV3C2BP · pith_short_8: 6X4GRJ6W

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/6X4GRJ6WKCV3C2BPLEO6NAPQ3G \
  | 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: f5f868a7d650abb1682f591de681f0d9af4747a9d70e59e7c698785e7a19cb83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c6db84342087dfa41725f8d9c5a935a83a4143c79d1c9aa1f3dbe1ba089ab49",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-22T21:48:26Z",
    "title_canon_sha256": "c334258b389845708c753f3748277c582d2ff9f6e88b4cb1813649a3ea7c58bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5911",
    "kind": "arxiv",
    "version": 1
  }
}