Pith Number

pith:U7DNPPQT

pith:2009:U7DNPPQTQD5FYFQ4N4Y27ESDDF

not attested not anchored not stored refs pending

On arithmetic in Mordell-Weil groups

Grzegorz Banaszak, Piotr Krason

arxiv:0904.2848 v3 · 2009-04-18 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U7DNPPQTQD5FYFQ4N4Y27ESDDF}

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	2026-05-18T04:42:35.353903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7c6d7be1380fa5c161c6f31af92431954ee97a40252ea89a4d01a4fb373cba3

Aliases

arxiv: 0904.2848 · arxiv_version: 0904.2848v3 · doi: 10.48550/arxiv.0904.2848 · pith_short_12: U7DNPPQTQD5F · pith_short_16: U7DNPPQTQD5FYFQ4 · pith_short_8: U7DNPPQT

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/U7DNPPQTQD5FYFQ4N4Y27ESDDF \
  | 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: a7c6d7be1380fa5c161c6f31af92431954ee97a40252ea89a4d01a4fb373cba3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ace0289ea9426577332e321bfdcef301947b367ea03436e7506ef9ba486f37f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-04-18T12:45:38Z",
    "title_canon_sha256": "574d7623dced44e098c0194c703618b5885aa7e8546f56d9e62a28591590a414"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.2848",
    "kind": "arxiv",
    "version": 3
  }
}