Pith Number

pith:6MSSQKIE

pith:2010:6MSSQKIEQ5LPG53GEP55KECVTB

not attested not anchored not stored refs pending

Density of rational points on elliptic surfaces

Ronald van Luijk

arxiv:1009.4306 v1 · 2010-09-22 · math.AG · 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{6MSSQKIEQ5LPG53GEP55KECVTB}

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	2026-05-18T04:40:33.422726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3252829048756f3776623fbd51055985ff200d9ed7aac060f319d5999a987d8

Aliases

arxiv: 1009.4306 · arxiv_version: 1009.4306v1 · doi: 10.48550/arxiv.1009.4306 · pith_short_12: 6MSSQKIEQ5LP · pith_short_16: 6MSSQKIEQ5LPG53G · pith_short_8: 6MSSQKIE

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/6MSSQKIEQ5LPG53GEP55KECVTB \
  | 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: f3252829048756f3776623fbd51055985ff200d9ed7aac060f319d5999a987d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13ea39b5ebd68765392548a2320cda88818015207db59850b73a9a69f9881fb9",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-09-22T09:31:20Z",
    "title_canon_sha256": "e4c85508b96cb66ba30885efb3591c1fad2958fd92dade3ce5a04f3a541890e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4306",
    "kind": "arxiv",
    "version": 1
  }
}