Pith Number

pith:EJQOWNH5

pith:2010:EJQOWNH52HMM5D2JZQHH7TFKOP

not attested not anchored not stored refs pending

Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one

R. L. Miller

arxiv:1010.2431 v3 · 2010-10-12 · 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{EJQOWNH52HMM5D2JZQHH7TFKOP}

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	2026-05-18T04:05:57.863839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2260eb34fdd1d8ce8f49cc0e7fccaa73e7ed0d0462aa510e70be9ecca4b0bdad

Aliases

arxiv: 1010.2431 · arxiv_version: 1010.2431v3 · doi: 10.48550/arxiv.1010.2431 · pith_short_12: EJQOWNH52HMM · pith_short_16: EJQOWNH52HMM5D2J · pith_short_8: EJQOWNH5

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/EJQOWNH52HMM5D2JZQHH7TFKOP \
  | 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: 2260eb34fdd1d8ce8f49cc0e7fccaa73e7ed0d0462aa510e70be9ecca4b0bdad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cbfb6dbc26d7874c28d792b8be4891d85038d5b4687d0637d653c4d1f799871",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-10-12T16:11:42Z",
    "title_canon_sha256": "52e8c179efddaa74b8fb64c47ed7586ffcd26de9ca6096a1f27cd49bdd73b27c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2431",
    "kind": "arxiv",
    "version": 3
  }
}