Pith Number

pith:AP43A4X6

pith:2010:AP43A4X6NQN5PIPMKLOVXQ3NZ2

not attested not anchored not stored refs pending

Minimal number of points with bad reduction for elliptic curves over P^1

Johannes Sprang

arxiv:1007.4353 v2 · 2010-07-25 · 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{AP43A4X6NQN5PIPMKLOVXQ3NZ2}

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	2026-05-18T04:17:03.294210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03f9b072fe6c1bd7a1ec52dd5bc36dcea694a1b05f18adef08b6077b3b5e1625

Aliases

arxiv: 1007.4353 · arxiv_version: 1007.4353v2 · doi: 10.48550/arxiv.1007.4353 · pith_short_12: AP43A4X6NQN5 · pith_short_16: AP43A4X6NQN5PIPM · pith_short_8: AP43A4X6

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/AP43A4X6NQN5PIPMKLOVXQ3NZ2 \
  | 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: 03f9b072fe6c1bd7a1ec52dd5bc36dcea694a1b05f18adef08b6077b3b5e1625

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caf260ed16aeecbbaf7f520537633715c00c137f89f4a7050dae1cd38641437e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-07-25T21:39:31Z",
    "title_canon_sha256": "200ae85625784a329bcb67fa0eea3d81840912d450cdd59d71c059d5c1bbf94e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4353",
    "kind": "arxiv",
    "version": 2
  }
}