Pith Number

pith:F4FUZUBZ

pith:2015:F4FUZUBZVAFMPCPI6M4NQ244SM

not attested not anchored not stored refs pending

Isogenies of non-CM elliptic curves with rational $j$-invariants over number fields

Filip Najman

arxiv:1506.03127 v1 · 2015-06-09 · 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{F4FUZUBZVAFMPCPI6M4NQ244SM}

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	2026-05-18T01:55:31.460698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f0b4cd039a80ac789e8f338d86b9c93375fb6cc2b3bc57762fd17373fe35233

Aliases

arxiv: 1506.03127 · arxiv_version: 1506.03127v1 · doi: 10.48550/arxiv.1506.03127 · pith_short_12: F4FUZUBZVAFM · pith_short_16: F4FUZUBZVAFMPCPI · pith_short_8: F4FUZUBZ

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/F4FUZUBZVAFMPCPI6M4NQ244SM \
  | 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: 2f0b4cd039a80ac789e8f338d86b9c93375fb6cc2b3bc57762fd17373fe35233

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a82941ec612255badd5519848d56e57d7361b650d5662d9b34a1153126d0a60",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-06-09T23:01:42Z",
    "title_canon_sha256": "c1bb9cac07c0a8460fd6b87ced114af8988d0639d31059faed4034e3af4a03a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03127",
    "kind": "arxiv",
    "version": 1
  }
}