Pith Number

pith:XENFGUI3

pith:2013:XENFGUI3RWAPPWZWAU73I2LVVW

not attested not anchored not stored refs pending

Quadratic Twists of Elliptic Curves with 3-Selmer Rank 1

Zane Kun Li

arxiv:1311.5306 v1 · 2013-11-21 · 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{XENFGUI3RWAPPWZWAU73I2LVVW}

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	2026-05-18T03:00:12.196827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b91a53511b8d80f7db36053fb46975ad824664f7caeb185de683b59ade101dd2

Aliases

arxiv: 1311.5306 · arxiv_version: 1311.5306v1 · doi: 10.48550/arxiv.1311.5306 · pith_short_12: XENFGUI3RWAP · pith_short_16: XENFGUI3RWAPPWZW · pith_short_8: XENFGUI3

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/XENFGUI3RWAPPWZWAU73I2LVVW \
  | 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: b91a53511b8d80f7db36053fb46975ad824664f7caeb185de683b59ade101dd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b908c8189092e2dc41a635bed15aefef085c8c39bf2330fc8f522ca98aa6463",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-21T03:50:17Z",
    "title_canon_sha256": "47b32367f82e332cf5275ddc61fcde500033a7e24d1c69c5d6379fd2bca8bbfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5306",
    "kind": "arxiv",
    "version": 1
  }
}