Pith Number

pith:GJ2P5UWL

pith:2015:GJ2P5UWLBLEROBOC4VWDIZR55F

not attested not anchored not stored refs pending

The Birch and Swinnerton-Dyer Formula for Elliptic Curves of Analytic Rank One

Christopher Skinner, Dimitar Jetchev, Xin Wan

arxiv:1512.06894 v1 · 2015-12-21 · 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{GJ2P5UWLBLEROBOC4VWDIZR55F}

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	2026-05-18T01:23:53.533405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3274fed2cb0ac91705c2e56c34663de94674b114eaa7b8102676ca894bfbea06

Aliases

arxiv: 1512.06894 · arxiv_version: 1512.06894v1 · doi: 10.48550/arxiv.1512.06894 · pith_short_12: GJ2P5UWLBLER · pith_short_16: GJ2P5UWLBLEROBOC · pith_short_8: GJ2P5UWL

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/GJ2P5UWLBLEROBOC4VWDIZR55F \
  | 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: 3274fed2cb0ac91705c2e56c34663de94674b114eaa7b8102676ca894bfbea06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce358ab42e0f9891dbe819088d11cdaf82812ce428a6fa5ab828c6dac1593169",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-21T22:26:35Z",
    "title_canon_sha256": "7f865325f143b3c415fb89210cfb5bbae73d4e64828a4102db5b40afa6b5e638"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06894",
    "kind": "arxiv",
    "version": 1
  }
}