Pith Number

pith:G2C347S7

pith:2010:G2C347S7JOOASIVGJFPTE2QFJI

not attested not anchored not stored refs pending

Concentration points on two and three dimensional modular hyperbolas and applications

J. Cilleruelo, M. Z. Garaev

arxiv:1007.1526 v2 · 2010-07-09 · 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{G2C347S7JOOASIVGJFPTE2QFJI}

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	2026-05-18T04:39:27.640409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3685be7e5f4b9c0922a6495f326a054a1e828c128c819feb0f51d8da3c66fb16

Aliases

arxiv: 1007.1526 · arxiv_version: 1007.1526v2 · doi: 10.48550/arxiv.1007.1526 · pith_short_12: G2C347S7JOOA · pith_short_16: G2C347S7JOOASIVG · pith_short_8: G2C347S7

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/G2C347S7JOOASIVGJFPTE2QFJI \
  | 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: 3685be7e5f4b9c0922a6495f326a054a1e828c128c819feb0f51d8da3c66fb16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf46b2b35b5a2cb3b4a7b67c12df33d588031b845edd016c256c08b5df9e39b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-07-09T08:04:03Z",
    "title_canon_sha256": "fa0e26ac9d2d3cb0a4b3ac8e9b2ddd258bf89352fb01241a0b8573a0a7421063"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1526",
    "kind": "arxiv",
    "version": 2
  }
}