Pith Number

pith:25GOAD7K

pith:2018:25GOAD7KMEDI4V46PULT7B3ZXI

not attested not anchored not stored refs pending

Rank growth of elliptic curves in nonabelian extensions

Frank Thorne, Robert J. Lemke Oliver

arxiv:1810.04018 v1 · 2018-10-09 · 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{25GOAD7KMEDI4V46PULT7B3ZXI}

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	2026-05-18T00:03:44.081247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d74ce00fea61068e579e7d173f8779ba2a1e2bc510246098e3f0a39f54a39a9a

Aliases

arxiv: 1810.04018 · arxiv_version: 1810.04018v1 · doi: 10.48550/arxiv.1810.04018 · pith_short_12: 25GOAD7KMEDI · pith_short_16: 25GOAD7KMEDI4V46 · pith_short_8: 25GOAD7K

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/25GOAD7KMEDI4V46PULT7B3ZXI \
  | 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: d74ce00fea61068e579e7d173f8779ba2a1e2bc510246098e3f0a39f54a39a9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9612da8d61b99e0c67bba09786bb8891e9e7bc7bf07ccc14448d66f75398924f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-09T14:21:02Z",
    "title_canon_sha256": "a65ff8c056dde8cbb0dc333d668f2457ec84a7fba9a047fb7913f47b85be797d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.04018",
    "kind": "arxiv",
    "version": 1
  }
}