Pith Number

pith:XFAQ55HY

pith:2012:XFAQ55HYELAYF3DMDN64IHQ3GE

not attested not anchored not stored refs pending

A Family of Elliptic Curves with a Lower Bound on 2-Selmer Ranks of Quadratic Twists

Zev Klagsbrun

arxiv:1201.5407 v3 · 2012-01-25 · 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{XFAQ55HYELAYF3DMDN64IHQ3GE}

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	2026-05-18T03:42:44.591842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9410ef4f822c182ec6c1b7dc41e1b3123d5237e25fa6256e15f9023f26a32d0

Aliases

arxiv: 1201.5407 · arxiv_version: 1201.5407v3 · doi: 10.48550/arxiv.1201.5407 · pith_short_12: XFAQ55HYELAY · pith_short_16: XFAQ55HYELAYF3DM · pith_short_8: XFAQ55HY

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/XFAQ55HYELAYF3DMDN64IHQ3GE \
  | 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: b9410ef4f822c182ec6c1b7dc41e1b3123d5237e25fa6256e15f9023f26a32d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6a67080c6b8442ab39680f8258e1ed611a81a6d54caa7012136c3aa74e98935",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-01-25T22:50:52Z",
    "title_canon_sha256": "ab324cadf268d5a8dc20f2931354bd8f921b7efd2ad9e48c476db87dc6f0e111"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.5407",
    "kind": "arxiv",
    "version": 3
  }
}