Pith Number

pith:OU4OQXEK

pith:2016:OU4OQXEKJL27LLLR5D3KMMG5TH

not attested not anchored not stored refs pending

High rank quadratic twists of pairs of elliptic curves

Mohamed Alaa, Mohammad Sadek

arxiv:1610.07967 v1 · 2016-10-25 · 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{OU4OQXEKJL27LLLR5D3KMMG5TH}

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	2026-05-18T00:53:12.043613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7538e85c8a4af5f5ad71e8f6a630dd99d0b626c016afe16e148d15774f198e6d

Aliases

arxiv: 1610.07967 · arxiv_version: 1610.07967v1 · doi: 10.48550/arxiv.1610.07967 · pith_short_12: OU4OQXEKJL27 · pith_short_16: OU4OQXEKJL27LLLR · pith_short_8: OU4OQXEK

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/OU4OQXEKJL27LLLR5D3KMMG5TH \
  | 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: 7538e85c8a4af5f5ad71e8f6a630dd99d0b626c016afe16e148d15774f198e6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "239c504ed3ff6a32738a519a254e87d867f5dc56043f0606be326aec36924f0d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-25T17:10:57Z",
    "title_canon_sha256": "21d9ba4f05990b1952e440b51a3c1bd9e7f316b6e072cd3623e575976148bf74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.07967",
    "kind": "arxiv",
    "version": 1
  }
}