Pith Number

pith:CS3DNDKQ

pith:2016:CS3DNDKQBMLSFPFLKRISBBHYHC

not attested not anchored not stored refs pending

Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves

Andrzej D\k{a}browski, Lucjan Szymaszkiewicz

arxiv:1611.08181 v1 · 2016-11-24 · 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{CS3DNDKQBMLSFPFLKRISBBHYHC}

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	2026-05-18T00:56:44.081305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14b6368d500b1722bcab54512084f8389e55276bd403f307d357c014769e3c21

Aliases

arxiv: 1611.08181 · arxiv_version: 1611.08181v1 · doi: 10.48550/arxiv.1611.08181 · pith_short_12: CS3DNDKQBMLS · pith_short_16: CS3DNDKQBMLSFPFL · pith_short_8: CS3DNDKQ

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/CS3DNDKQBMLSFPFLKRISBBHYHC \
  | 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: 14b6368d500b1722bcab54512084f8389e55276bd403f307d357c014769e3c21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a431ae9604910913ff86f4a1ad4ff3260b511b66e3a12d44b311cbecd7067d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-11-24T13:43:30Z",
    "title_canon_sha256": "73766598f23674b7699b5a5501ba2919631008b19590dab198db545d4e387e36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.08181",
    "kind": "arxiv",
    "version": 1
  }
}