Pith Number

pith:5VK3RVVO

pith:2017:5VK3RVVOQGTPUM7OJP55D5YZRU

not attested not anchored not stored refs pending

Torsion subgroups of rational elliptic curves over the compositum of all $D_4$ extensions of the rational numbers

Harris B. Daniels

arxiv:1710.05228 v4 · 2017-10-14 · 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{5VK3RVVOQGTPUM7OJP55D5YZRU}

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	2026-05-18T00:23:13.892435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed55b8d6ae81a6fa33ee4bfbd1f7198d1f6d6fcadfb41be96893f6d31af832a6

Aliases

arxiv: 1710.05228 · arxiv_version: 1710.05228v4 · doi: 10.48550/arxiv.1710.05228 · pith_short_12: 5VK3RVVOQGTP · pith_short_16: 5VK3RVVOQGTPUM7O · pith_short_8: 5VK3RVVO

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/5VK3RVVOQGTPUM7OJP55D5YZRU \
  | 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: ed55b8d6ae81a6fa33ee4bfbd1f7198d1f6d6fcadfb41be96893f6d31af832a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acc78f31a0382c6d5708d9b6f23dbb066dddbf636307d4535dc15da949aaced9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-10-14T19:53:44Z",
    "title_canon_sha256": "6abf14b6764e6e17a52750cc470442d7cec7c68b1fed8a09d32ca217e4cb2913"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.05228",
    "kind": "arxiv",
    "version": 4
  }
}