Pith Number

pith:ZSOIUZML

pith:2015:ZSOIUZMLKZ4P6BBHOKRGIOMN3F

not attested not anchored not stored refs pending

Torsion subgroups of rational elliptic curves over the compositum of all cubic fields

Alvaro Lozano-Robledo, Andrew V. Sutherland, Filip Najman, Harris B. Daniels

arxiv:1509.00528 v5 · 2015-09-02 · 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{ZSOIUZMLKZ4P6BBHOKRGIOMN3F}

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	2026-05-18T00:25:06.027765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc9c8a658b5678ff042772a264398dd94ee77f658c5040df552912332018eea8

Aliases

arxiv: 1509.00528 · arxiv_version: 1509.00528v5 · doi: 10.48550/arxiv.1509.00528 · pith_short_12: ZSOIUZMLKZ4P · pith_short_16: ZSOIUZMLKZ4P6BBH · pith_short_8: ZSOIUZML

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/ZSOIUZMLKZ4P6BBHOKRGIOMN3F \
  | 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: cc9c8a658b5678ff042772a264398dd94ee77f658c5040df552912332018eea8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5e4aa36795b3f6571ccdcd350cba5f287a91a374e37b7a743463c931342e961",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-02T00:10:16Z",
    "title_canon_sha256": "05b753764d2042bf2d1058a2ad7382d859a3e2951f98f4ac0cc7bb114b0f550f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00528",
    "kind": "arxiv",
    "version": 5
  }
}