Pith Number

pith:M62N5MGJ

pith:2021:M62N5MGJHAZTRLPMH4LG2WA3NA

not attested not anchored not stored refs pending

On the Selmer group and rank of a family of elliptic curves and curves of genus one violating the Hasse principle

Eleni Agathocleous

arxiv:2111.03723 v7 · 2021-11-05 · 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{M62N5MGJHAZTRLPMH4LG2WA3NA}

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	2026-07-05T09:05:58.802213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67b4deb0c9383338adec3f166d581b6820a749cc61f3b7d96fdb5534dc62d61a

Aliases

arxiv: 2111.03723 · arxiv_version: 2111.03723v7 · doi: 10.48550/arxiv.2111.03723 · pith_short_12: M62N5MGJHAZT · pith_short_16: M62N5MGJHAZTRLPM · pith_short_8: M62N5MGJ

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/M62N5MGJHAZTRLPMH4LG2WA3NA \
  | 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: 67b4deb0c9383338adec3f166d581b6820a749cc61f3b7d96fdb5534dc62d61a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8c74ebbd090f8ac73507de81b663cb4e73dd3c63e04363811cfd588011aa8d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-11-05T20:40:46Z",
    "title_canon_sha256": "909d2001743fd5bd24b6ec70d33a912c6528b2f11ed2f2f93c669ef295ea3ce5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.03723",
    "kind": "arxiv",
    "version": 7
  }
}