Pith Number

pith:KQQKAVWH

pith:2025:KQQKAVWHPCJ4UWWBQCYNLITKLK

not attested not anchored not stored refs pending

Infinitely many pairs of non-isomorphic elliptic curves sharing the same BSD invariants

Asuka Shiga

arxiv:2507.18574 v2 · 2025-07-24 · 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{KQQKAVWHPCJ4UWWBQCYNLITKLK}

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	2026-07-05T11:56:59.549372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5420a056c77893ca5ac180b0d5a26a5a9b0bbc08e30a31b48eaab83150137940

Aliases

arxiv: 2507.18574 · arxiv_version: 2507.18574v2 · doi: 10.48550/arxiv.2507.18574 · pith_short_12: KQQKAVWHPCJ4 · pith_short_16: KQQKAVWHPCJ4UWWB · pith_short_8: KQQKAVWH

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/KQQKAVWHPCJ4UWWBQCYNLITKLK \
  | 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: 5420a056c77893ca5ac180b0d5a26a5a9b0bbc08e30a31b48eaab83150137940

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff7e831a658f9686f2bca411db01bacfb13a6883885cb1e7f4bf2cf8d302529e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-07-24T16:47:50Z",
    "title_canon_sha256": "e260bf88268efbdc1f5b8f61584250d0f0c45f0f8c4b94b05e7903338a273453"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.18574",
    "kind": "arxiv",
    "version": 2
  }
}