Pith Number

pith:D3KEEIZQ

pith:2011:D3KEEIZQFZ5U7TQ34HMLPPCVEX

not attested not anchored not stored refs pending

Catalan's Equation For Even Primes over Quadratic Fields

Prem Prakash Pandey, R. Balasubramanian

arxiv:1112.2688 v3 · 2011-12-12 · 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{D3KEEIZQFZ5U7TQ34HMLPPCVEX}

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	2026-05-18T01:26:03.283959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ed44223302e7b4fce1be1d8b7bc5525f75dc4886c4eab2d7b8227621028b218

Aliases

arxiv: 1112.2688 · arxiv_version: 1112.2688v3 · doi: 10.48550/arxiv.1112.2688 · pith_short_12: D3KEEIZQFZ5U · pith_short_16: D3KEEIZQFZ5U7TQ3 · pith_short_8: D3KEEIZQ

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/D3KEEIZQFZ5U7TQ34HMLPPCVEX \
  | 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: 1ed44223302e7b4fce1be1d8b7bc5525f75dc4886c4eab2d7b8227621028b218

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d5e0e7f3e451b3d45bc934e204f307454964d3f0986455cad073e060a4dbc40",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-12T20:35:18Z",
    "title_canon_sha256": "065a37c04398e5a7dae304a3809ca92197b5e0c3031ee54357a9be13896f40f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2688",
    "kind": "arxiv",
    "version": 3
  }
}