Pith Number

pith:5I57TKTM

pith:2012:5I57TKTMR7FZDBM5OEKBFCTEBU

not attested not anchored not stored refs pending

The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point

Benedict H. Gross, Manjul Bhargava

arxiv:1208.1007 v2 · 2012-08-05 · 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{5I57TKTMR7FZDBM5OEKBFCTEBU}

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	2026-05-18T03:27:01.551830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea3bf9aa6c8fcb91859d7114128a640d2c6c1a4a04f47ff8c76e1c05154f7302

Aliases

arxiv: 1208.1007 · arxiv_version: 1208.1007v2 · doi: 10.48550/arxiv.1208.1007 · pith_short_12: 5I57TKTMR7FZ · pith_short_16: 5I57TKTMR7FZDBM5 · pith_short_8: 5I57TKTM

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/5I57TKTMR7FZDBM5OEKBFCTEBU \
  | 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: ea3bf9aa6c8fcb91859d7114128a640d2c6c1a4a04f47ff8c76e1c05154f7302

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb0bf92e97943b7ca40b6dfe64e030010c0c5b1bf86af7a6ac0c34b951ccf179",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-05T13:16:19Z",
    "title_canon_sha256": "f0e2496e8e02df04505a0ccae63afaa72a6ffe6c2ab1ac617c79046f38128fbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1007",
    "kind": "arxiv",
    "version": 2
  }
}