Pith Number

pith:MMU3GWP6

pith:2013:MMU3GWP6XO73Q4ZTMUVTRJWIBT

not attested not anchored not stored refs pending

On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication

Chunlai Zhao, John Coates, Minhyong Kim, ZhiBin Liang

arxiv:1303.5218 v2 · 2013-03-21 · 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{MMU3GWP6XO73Q4ZTMUVTRJWIBT}

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	2026-05-18T03:28:45.271900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6329b359febbbfb87333652b38a6c80cead3de3336565931b4bb9f1de44adde7

Aliases

arxiv: 1303.5218 · arxiv_version: 1303.5218v2 · doi: 10.48550/arxiv.1303.5218 · pith_short_12: MMU3GWP6XO73 · pith_short_16: MMU3GWP6XO73Q4ZT · pith_short_8: MMU3GWP6

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/MMU3GWP6XO73Q4ZTMUVTRJWIBT \
  | 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: 6329b359febbbfb87333652b38a6c80cead3de3336565931b4bb9f1de44adde7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0ba9dcdb7fda9a9c5c97c3ce2b21553673ac304d2f42d8e865998dcb13f2a53",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-03-21T10:22:51Z",
    "title_canon_sha256": "3af08cfce34897c34224f7bd68fe61500e758fde4e3a312d6811c6ce2fca0a4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5218",
    "kind": "arxiv",
    "version": 2
  }
}