Pith Number

pith:L7WOY2QZ

pith:2012:L7WOY2QZHOQRJJ456X5WEI32YI

not attested not anchored not stored refs pending

Constructing non-trivial elements of the Shafarevich-Tate group of an Abelian Variety over a Number Field

Amod Agashe, Saikat Biswas

arxiv:1201.2310 v2 · 2012-01-11 · 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{L7WOY2QZHOQRJJ456X5WEI32YI}

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	2026-05-18T03:06:05.743738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fecec6a193ba114a79df5fb62237ac2327ba37a11e13dd70b90579068f2ddd2

Aliases

arxiv: 1201.2310 · arxiv_version: 1201.2310v2 · doi: 10.48550/arxiv.1201.2310 · pith_short_12: L7WOY2QZHOQR · pith_short_16: L7WOY2QZHOQRJJ45 · pith_short_8: L7WOY2QZ

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/L7WOY2QZHOQRJJ456X5WEI32YI \
  | 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: 5fecec6a193ba114a79df5fb62237ac2327ba37a11e13dd70b90579068f2ddd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90da33b563667aef23bab4187ec289a317ec9c98fa094a0c6f6e87e152283b43",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-01-11T14:40:36Z",
    "title_canon_sha256": "39c38ebde16427514f8acc1b0791c5fab470014046929598249e763e78ec1834"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2310",
    "kind": "arxiv",
    "version": 2
  }
}