Pith Number

pith:5QGDHW6Y

pith:2021:5QGDHW6Y7DHJ4JB7TYVWCFTUHF

not attested not anchored not stored refs pending

Typically bounding torsion on elliptic curves isogenous to rational $j$-invariant

Tyler Genao

arxiv:2112.11566 v2 · 2021-12-21 · 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{5QGDHW6Y7DHJ4JB7TYVWCFTUHF}

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

Minimal torsion curves in geometric isogeny classes

Receipt and verification

First computed	2026-07-05T05:06:53.907119Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec0c33dbd8f8ce9e243f9e2b6116743971bdecd4eae2797cb8037cecc6cffbab

Aliases

arxiv: 2112.11566 · arxiv_version: 2112.11566v2 · doi: 10.48550/arxiv.2112.11566 · pith_short_12: 5QGDHW6Y7DHJ · pith_short_16: 5QGDHW6Y7DHJ4JB7 · pith_short_8: 5QGDHW6Y

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/5QGDHW6Y7DHJ4JB7TYVWCFTUHF \
  | 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: ec0c33dbd8f8ce9e243f9e2b6116743971bdecd4eae2797cb8037cecc6cffbab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fba15f1bc9d4d295dc776dcb084d0026978c740e8438e352c9241b9a5c178e99",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-12-21T22:59:42Z",
    "title_canon_sha256": "8f3f03ebacaec3c7aa1f4e576bf281d8b79d0f7fcf96916d92ede08549616eda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.11566",
    "kind": "arxiv",
    "version": 2
  }
}