Pith Number

pith:TQSO3GM4

pith:2012:TQSO3GM4FAQXV73QYH7HQXMFF5

not attested not anchored not stored refs pending

The growth of the rank of Abelian varieties upon extensions

Filip Najman, Peter Bruin

arxiv:1210.6085 v1 · 2012-10-22 · 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{TQSO3GM4FAQXV73QYH7HQXMFF5}

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	2026-05-18T03:42:33.323553Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c24ed999c28217aff70c1fe785d852f7f0b70b027351e12b4608fd7f96aafda

Aliases

arxiv: 1210.6085 · arxiv_version: 1210.6085v1 · doi: 10.48550/arxiv.1210.6085 · pith_short_12: TQSO3GM4FAQX · pith_short_16: TQSO3GM4FAQXV73Q · pith_short_8: TQSO3GM4

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/TQSO3GM4FAQXV73QYH7HQXMFF5 \
  | 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: 9c24ed999c28217aff70c1fe785d852f7f0b70b027351e12b4608fd7f96aafda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cfd4ba6e67b8ff28bfea050aec0ebc53678f1ef3a6eee0eaee410f6f3fb72fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-22T23:05:07Z",
    "title_canon_sha256": "1260103b70ddcdf4f6002cf6f553902bc3036bd640b4792bc0d514528f787125"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6085",
    "kind": "arxiv",
    "version": 1
  }
}