Pith Number

pith:PP2TQJFP

pith:2018:PP2TQJFPO7LYKNYNWP3UMIH234

not attested not anchored not stored refs pending

On the non-vanishing of generalized Kato classes for elliptic curves of rank $2$

Francesc Castella, Ming-Lun Hsieh

arxiv:1809.09066 v4 · 2018-09-24 · 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{PP2TQJFPO7LYKNYNWP3UMIH234}

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	2026-05-17T23:41:01.150032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bf53824af77d785370db3f74620fadf1daecf1f33bfe69244f118894c6f818a

Aliases

arxiv: 1809.09066 · arxiv_version: 1809.09066v4 · doi: 10.48550/arxiv.1809.09066 · pith_short_12: PP2TQJFPO7LY · pith_short_16: PP2TQJFPO7LYKNYN · pith_short_8: PP2TQJFP

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/PP2TQJFPO7LYKNYNWP3UMIH234 \
  | 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: 7bf53824af77d785370db3f74620fadf1daecf1f33bfe69244f118894c6f818a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38c26fe15202531aa51e92cc820b67cd5bcc743339ac389bbeb5a731491738ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-09-24T17:18:34Z",
    "title_canon_sha256": "27ba38735c4fe644eefb1e0ac1f04de1acb148be66fbf861c4549b7d1586aad0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.09066",
    "kind": "arxiv",
    "version": 4
  }
}