Pith Number

pith:KTR5ZKE5

pith:2014:KTR5ZKE5TI2GDUQG6YARCFISCA

not attested not anchored not stored refs pending

The average number of integral points on elliptic curves is bounded

Levent Alpoge

arxiv:1412.1047 v3 · 2014-12-02 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KTR5ZKE5TI2GDUQG6YARCFISCA}

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.

Cited by

1 paper in Pith

Additive Rigidity for $x$-Coordinates of Rational Points on Elliptic Curves

Receipt and verification

First computed	2026-05-18T02:27:31.834254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54e3dca89d9a3461d206f601111512101609cc7c2a15d29744b7e48ada73b8fa

Aliases

arxiv: 1412.1047 · arxiv_version: 1412.1047v3 · doi: 10.48550/arxiv.1412.1047 · pith_short_12: KTR5ZKE5TI2G · pith_short_16: KTR5ZKE5TI2GDUQG · pith_short_8: KTR5ZKE5

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/KTR5ZKE5TI2GDUQG6YARCFISCA \
  | 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: 54e3dca89d9a3461d206f601111512101609cc7c2a15d29744b7e48ada73b8fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83b41f2cfb276bf839b4260c1e427df39edd3edc1a44a95ac2ed0d8670746cab",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-12-02T20:07:01Z",
    "title_canon_sha256": "2005e165ebd6066d3d3ae1fef8a041d3fec860c26496ed61dd1be8a0f0e42d8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.1047",
    "kind": "arxiv",
    "version": 3
  }
}