Pith Number

pith:35G4KL6C

pith:2011:35G4KL6CSU7HQRHKN3WDLKHGS3

not attested not anchored not stored refs pending

Minimisation and reduction of 5-coverings of elliptic curves

Tom Fisher

arxiv:1112.5131 v1 · 2011-12-21 · 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{35G4KL6CSU7HQRHKN3WDLKHGS3}

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	2026-05-18T04:05:56.144372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df4dc52fc2953e7844ea6eec35a8e696cdeb95d1ab9fe6fb8e068084074c60b7

Aliases

arxiv: 1112.5131 · arxiv_version: 1112.5131v1 · doi: 10.48550/arxiv.1112.5131 · pith_short_12: 35G4KL6CSU7H · pith_short_16: 35G4KL6CSU7HQRHK · pith_short_8: 35G4KL6C

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/35G4KL6CSU7HQRHKN3WDLKHGS3 \
  | 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: df4dc52fc2953e7844ea6eec35a8e696cdeb95d1ab9fe6fb8e068084074c60b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0591faffaeeba037521c01a18b5888d21dd6feeaa8f1aaa491e1578f373658ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-21T18:53:03Z",
    "title_canon_sha256": "9070b0424e37ebf0a56ad86247ef587c3409aa6d7e1a1c50b24719f1dd18a4da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5131",
    "kind": "arxiv",
    "version": 1
  }
}