Pith Number

pith:CVKC3Q4Z

pith:2012:CVKC3Q4ZLTHKA53T3RGKWDPQEO

not attested not anchored not stored refs pending

Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples

Bartosz Naskr\k{e}cki

arxiv:1210.6933 v2 · 2012-10-25 · 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{CVKC3Q4ZLTHKA53T3RGKWDPQEO}

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	2026-05-18T02:47:41.373174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15542dc3995ccea07773dc4cab0df023bcdb5813ca0439b8c810e99e7a3539c1

Aliases

arxiv: 1210.6933 · arxiv_version: 1210.6933v2 · doi: 10.48550/arxiv.1210.6933 · pith_short_12: CVKC3Q4ZLTHK · pith_short_16: CVKC3Q4ZLTHKA53T · pith_short_8: CVKC3Q4Z

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/CVKC3Q4ZLTHKA53T3RGKWDPQEO \
  | 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: 15542dc3995ccea07773dc4cab0df023bcdb5813ca0439b8c810e99e7a3539c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a0a3cb17bf6e682b70f0d4bdc31f91b252fa1e7cbb0ab23a28a082746dba702",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-25T18:23:21Z",
    "title_canon_sha256": "ba4de3affa6668e4c76ffd537ce00d2ed05d3797fdd76626137201c2f2911878"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6933",
    "kind": "arxiv",
    "version": 2
  }
}