Pith Number

pith:U2PYXBLJ

pith:2009:U2PYXBLJJIZWCVF3DPTSKYARNO

not attested not anchored not stored refs pending

The Brauer group of Kummer surfaces and torsion of elliptic curves

Alexei N. Skorobogatov, Yuri G. Zarhin

arxiv:0911.2261 v2 · 2009-11-11 · 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{U2PYXBLJJIZWCVF3DPTSKYARNO}

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	2026-05-18T04:36:50.363303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a69f8b85694a336154bb1be72560116b81cf0702c8b788f4a1e0e8ad7ef518a4

Aliases

arxiv: 0911.2261 · arxiv_version: 0911.2261v2 · doi: 10.48550/arxiv.0911.2261 · pith_short_12: U2PYXBLJJIZW · pith_short_16: U2PYXBLJJIZWCVF3 · pith_short_8: U2PYXBLJ

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/U2PYXBLJJIZWCVF3DPTSKYARNO \
  | 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: a69f8b85694a336154bb1be72560116b81cf0702c8b788f4a1e0e8ad7ef518a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99f21e0bf5826f6294840e200465c5fbf3076caa0586a7182da4936866397896",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-11-11T22:24:30Z",
    "title_canon_sha256": "8e2d410bfa366e5b3a0b5a9b16f40aff9714b36eaa46661c3c2e7961589e656a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2261",
    "kind": "arxiv",
    "version": 2
  }
}