Pith Number

pith:DIHSL5PT

pith:2018:DIHSL5PTQOREEYLNYMIERHWMCV

not attested not anchored not stored refs pending

Ranks, $2$-Selmer groups, and Tamagawa numbers of elliptic curves with $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/8\mathbb{Z}$-torsion

Jeroen Hanselman, Stephanie Chan, Wanlin Li

arxiv:1805.10709 v2 · 2018-05-27 · 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{DIHSL5PTQOREEYLNYMIERHWMCV}

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	2026-05-17T23:54:11.435362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a0f25f5f383a242616dc310489ecc154eca375cee60b9264421e71fd06bef90

Aliases

arxiv: 1805.10709 · arxiv_version: 1805.10709v2 · doi: 10.48550/arxiv.1805.10709 · pith_short_12: DIHSL5PTQORE · pith_short_16: DIHSL5PTQOREEYLN · pith_short_8: DIHSL5PT

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/DIHSL5PTQOREEYLNYMIERHWMCV \
  | 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: 1a0f25f5f383a242616dc310489ecc154eca375cee60b9264421e71fd06bef90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef720ed4879ea486a9335570969cd4ce7a5de8665f266b6ab6c7e3f10b3b0c19",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-05-27T23:02:46Z",
    "title_canon_sha256": "a7c752cc05103482c11d7bc5e9dd188c9a8594da9aa1c990b92608b83c57a60b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.10709",
    "kind": "arxiv",
    "version": 2
  }
}