Pith Number

pith:3SAJF2A4

pith:2026:3SAJF2A4DTBZMYOWJNE66TNOMO

not attested not anchored not stored refs pending

Exact classification of elliptic curves $y^{2}=x^{3}-pqx$ with rank $0$ and trivial $\Sha[2]$

Arkabrata Ghosh, Paul M. Voutier

arxiv:2607.14033 v1 · 2026-07-15 · 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{3SAJF2A4DTBZMYOWJNE66TNOMO}

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	2026-07-16T01:23:20.764106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc8092e81c1cc39661d64b49ef4dae63bfd83f45a9fa09ba93cc42ab9478457d

Aliases

arxiv: 2607.14033 · arxiv_version: 2607.14033v1 · doi: 10.48550/arxiv.2607.14033 · pith_short_12: 3SAJF2A4DTBZ · pith_short_16: 3SAJF2A4DTBZMYOW · pith_short_8: 3SAJF2A4

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/3SAJF2A4DTBZMYOWJNE66TNOMO \
  | 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: dc8092e81c1cc39661d64b49ef4dae63bfd83f45a9fa09ba93cc42ab9478457d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03bce01f7b15b9f8225d37cf8885e2267c6e8c1c878465fcccca835a8e47b09f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-15T17:02:21Z",
    "title_canon_sha256": "c09e723011a27c20f7c85a24b546990f64cd5e4b9b2127f5bf17121b7b7c27eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14033",
    "kind": "arxiv",
    "version": 1
  }
}