Pith Number

pith:VCBICABS

pith:2010:VCBICABSB6OLKJLJK4RJVPTRBM

not attested not anchored not stored refs pending

On quadratic twists of elliptic curves and some applications of a refined version of Yu's formula

Derong Qiu

arxiv:1003.4393 v3 · 2010-03-23 · 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{VCBICABSB6OLKJLJK4RJVPTRBM}

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	2026-05-18T02:48:53.607630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8828100320f9cb5256957229abe710b299bf5049e366811995a9de3df8cfeb9

Aliases

arxiv: 1003.4393 · arxiv_version: 1003.4393v3 · doi: 10.48550/arxiv.1003.4393 · pith_short_12: VCBICABSB6OL · pith_short_16: VCBICABSB6OLKJLJ · pith_short_8: VCBICABS

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/VCBICABSB6OLKJLJK4RJVPTRBM \
  | 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: a8828100320f9cb5256957229abe710b299bf5049e366811995a9de3df8cfeb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3678aafc895dff38f27373975137a7d6ef7535a11bca68810ce6cba93027f84",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-03-23T12:27:29Z",
    "title_canon_sha256": "4ef2a81e14b37f66d5958949f274ecacae9ad6b751f8337455a2a9bae49d5a0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.4393",
    "kind": "arxiv",
    "version": 3
  }
}