Pith Number

pith:XZ3MJT2A

pith:2009:XZ3MJT2ADEZ6MRMVVMSJDEY2IN

not attested not anchored not stored refs pending

A note on the Mordell-Weil rank modulo n

Tim Dokchitser, Vladimir Dokchitser

arxiv:0910.4588 v1 · 2009-10-23 · 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{XZ3MJT2ADEZ6MRMVVMSJDEY2IN}

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	2026-05-18T03:12:48.814811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be76c4cf401933e64595ab2491931a4362550088fea8566108e31d4c34b9091c

Aliases

arxiv: 0910.4588 · arxiv_version: 0910.4588v1 · doi: 10.48550/arxiv.0910.4588 · pith_short_12: XZ3MJT2ADEZ6 · pith_short_16: XZ3MJT2ADEZ6MRMV · pith_short_8: XZ3MJT2A

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/XZ3MJT2ADEZ6MRMVVMSJDEY2IN \
  | 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: be76c4cf401933e64595ab2491931a4362550088fea8566108e31d4c34b9091c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8710e549239adf7303d2609eedb502b49f6aab690951911807347e129aee265",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-10-23T20:16:14Z",
    "title_canon_sha256": "62e611430b0a07cdad8ec5885e6d8c35095313ae339949b71ad5b51ded5aba09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.4588",
    "kind": "arxiv",
    "version": 1
  }
}