Pith Number

pith:JI4WGZHF

pith:2016:JI4WGZHFI445SLGJTPJJG5PGIA

not attested not anchored not stored refs pending

Distribution of Mordell--Weil ranks of families of elliptic curves

Bartosz Naskr\k{e}cki

arxiv:1609.04731 v1 · 2016-09-15 · 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{JI4WGZHFI445SLGJTPJJG5PGIA}

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	2026-05-18T01:04:35.725161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a396364e54739d92cc99bd29375e6403cd48e755f180d91a21440cc3b9269dc

Aliases

arxiv: 1609.04731 · arxiv_version: 1609.04731v1 · doi: 10.48550/arxiv.1609.04731 · pith_short_12: JI4WGZHFI445 · pith_short_16: JI4WGZHFI445SLGJ · pith_short_8: JI4WGZHF

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/JI4WGZHFI445SLGJTPJJG5PGIA \
  | 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: 4a396364e54739d92cc99bd29375e6403cd48e755f180d91a21440cc3b9269dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ffd57d10fb9d4758ae4435d7fc1c3842f908c4bf8f1e4badccdde6287083adfc",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-15T16:47:06Z",
    "title_canon_sha256": "8ca1c58d48d7527b376ceb65bdb56e9ad08d032d175100f7fd7e155eb0e9b787"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.04731",
    "kind": "arxiv",
    "version": 1
  }
}