Pith Number

pith:QIHXJHR7

pith:2011:QIHXJHR77FMGR45BDDOYKW3HMN

not attested not anchored not stored refs pending

Ranks of elliptic curves with prescribed torsion over number fields

Andrej Dujella, Filip Najman, Johan Bosman, Peter Bruin

arxiv:1201.0252 v1 · 2011-12-31 · 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{QIHXJHR77FMGR45BDDOYKW3HMN}

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	2026-05-18T02:51:15.314779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

820f749e3ff95868f3a118dd855b676362e753baa7dd421e0bfc3d7892615c7e

Aliases

arxiv: 1201.0252 · arxiv_version: 1201.0252v1 · doi: 10.48550/arxiv.1201.0252 · pith_short_12: QIHXJHR77FMG · pith_short_16: QIHXJHR77FMGR45B · pith_short_8: QIHXJHR7

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/QIHXJHR77FMGR45BDDOYKW3HMN \
  | 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: 820f749e3ff95868f3a118dd855b676362e753baa7dd421e0bfc3d7892615c7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9559cb96062e522b2ca1e27578cdb8503d0716b36d5b0ee01793cdf46aebe47c",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-31T12:22:42Z",
    "title_canon_sha256": "d0ea30a3d5f63f84ec8bcf57563c0cb53c60fab1d607f1e6a73ddb5c08a0c6e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0252",
    "kind": "arxiv",
    "version": 1
  }
}