Pith Number

pith:FAH4XZAD

pith:2011:FAH4XZADMRQI4D7IWGFRAVTTVK

not attested not anchored not stored refs pending

Computing endomorphism rings of elliptic curves under the GRH

Gaetan Bisson

arxiv:1101.4323 v2 · 2011-01-22 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FAH4XZADMRQI4D7IWGFRAVTTVK}

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	2026-05-18T03:33:26.819354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

280fcbe40364608e0fe8b18b105673aaacee31ad224b1162dbcf9fee517ac100

Aliases

arxiv: 1101.4323 · arxiv_version: 1101.4323v2 · doi: 10.48550/arxiv.1101.4323 · pith_short_12: FAH4XZADMRQI · pith_short_16: FAH4XZADMRQI4D7I · pith_short_8: FAH4XZAD

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/FAH4XZADMRQI4D7IWGFRAVTTVK \
  | 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: 280fcbe40364608e0fe8b18b105673aaacee31ad224b1162dbcf9fee517ac100

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b07a1168c45381189204c6ed566bbc46bab76b01a48243679912876bfbf4cdca",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-22T21:08:26Z",
    "title_canon_sha256": "ae1cd580d2212d71f71bc40c5097437a5c6fc2fae4ff4347f3c930fb539f83c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4323",
    "kind": "arxiv",
    "version": 2
  }
}