Pith Number

pith:VDBFPFR2

pith:2013:VDBFPFR2G7KVZT6DU2YZTPRWSO

not attested not anchored not stored refs pending

Quadratic Twists of Elliptic Curves

John Coates, Shuai Zhai, Ye Tian, Yongxiong Li

arxiv:1312.3884 v3 · 2013-12-13 · 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{VDBFPFR2G7KVZT6DU2YZTPRWSO}

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	2026-05-18T02:44:56.767357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8c257963a37d55ccfc3a6b199be36939e3e140da4ff1b9054d68f5cea41d32e

Aliases

arxiv: 1312.3884 · arxiv_version: 1312.3884v3 · doi: 10.48550/arxiv.1312.3884 · pith_short_12: VDBFPFR2G7KV · pith_short_16: VDBFPFR2G7KVZT6D · pith_short_8: VDBFPFR2

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/VDBFPFR2G7KVZT6DU2YZTPRWSO \
  | 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: a8c257963a37d55ccfc3a6b199be36939e3e140da4ff1b9054d68f5cea41d32e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b6caf5fdc1c683632f1aab780169078d0cab0364c3786e14cd3e100a7a5e5ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-13T17:25:29Z",
    "title_canon_sha256": "9470c9daf0804513682abf0001ae6632530fec2bcc69e600a89301f01b1f3b85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3884",
    "kind": "arxiv",
    "version": 3
  }
}