Pith Number

pith:76OP7424

pith:2011:76OP7424KLL7BFKHBCGZ3UMNKG

not attested not anchored not stored refs pending

Weil-Ch\^atelet divisible elements in Tate-Shafarevich groups I: The Bashmakov problem for elliptic curves over Q

Jakob Stix, Mirela \c{C}iperiani

arxiv:1106.4255 v2 · 2011-06-21 · 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{76OP7424KLL7BFKHBCGZ3UMNKG}

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	2026-05-17T23:53:19.330520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff9cfff35c52d7f09547088d9dd18d518441d7275fdc7eba8fa6956fde7a1fa6

Aliases

arxiv: 1106.4255 · arxiv_version: 1106.4255v2 · doi: 10.48550/arxiv.1106.4255 · pith_short_12: 76OP7424KLL7 · pith_short_16: 76OP7424KLL7BFKH · pith_short_8: 76OP7424

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/76OP7424KLL7BFKHBCGZ3UMNKG \
  | 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: ff9cfff35c52d7f09547088d9dd18d518441d7275fdc7eba8fa6956fde7a1fa6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78fe62afc881a33bc9c0b93b9d0798d52931aa5976158c82bfc48d9b58f2106e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-06-21T16:37:18Z",
    "title_canon_sha256": "19f7f56480bbfad54f805f9ab0e7f84a77d039463c809d9b2367710c86a7bae1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4255",
    "kind": "arxiv",
    "version": 2
  }
}