Pith Number

pith:KS2Q6A4G

pith:2012:KS2Q6A4GEJAFB3DB5THVI4UPX4

not attested not anchored not stored refs pending

On p-torsion of p-adic elliptic curves with additive reduction

Ren\'e Pannekoek

arxiv:1211.5833 v2 · 2012-11-26 · 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{KS2Q6A4GEJAFB3DB5THVI4UPX4}

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.

Cited by

1 paper in Pith

Nontrivial torsion in the Tate--Shafarevich group of elliptic curves via visibility and twists

Receipt and verification

First computed	2026-05-18T03:35:01.617244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54b50f0386224050ec61eccf54728fbf3890e35f12d2279fa905db37eacc9e30

Aliases

arxiv: 1211.5833 · arxiv_version: 1211.5833v2 · doi: 10.48550/arxiv.1211.5833 · pith_short_12: KS2Q6A4GEJAF · pith_short_16: KS2Q6A4GEJAFB3DB · pith_short_8: KS2Q6A4G

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/KS2Q6A4GEJAFB3DB5THVI4UPX4 \
  | 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: 54b50f0386224050ec61eccf54728fbf3890e35f12d2279fa905db37eacc9e30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "987089ae7bc3d29fd1da3ed6cf58cc3aa1a7ca398c7eb19b8c1d5152e99212c0",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-11-26T01:26:06Z",
    "title_canon_sha256": "88dbca259eb2257d51f9cf85a5b10960d9ca1da27b468639718b63abcf3ea398"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5833",
    "kind": "arxiv",
    "version": 2
  }
}