Pith Number

pith:QJFFRCFQ

pith:2012:QJFFRCFQZQM6CUZIMCVJNY7PI3

not attested not anchored not stored refs pending

Integral Tate modules and splitting of primes in torsion fields of elliptic curves

Tommaso Giorgio Centeleghe

arxiv:1201.2124 v5 · 2012-01-10 · 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{QJFFRCFQZQM6CUZIMCVJNY7PI3}

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	2026-05-18T01:34:30.325189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

824a5888b0cc19e1532860aa96e3ef46e8094df2329c3e0df7fa4c04da597dad

Aliases

arxiv: 1201.2124 · arxiv_version: 1201.2124v5 · doi: 10.48550/arxiv.1201.2124 · pith_short_12: QJFFRCFQZQM6 · pith_short_16: QJFFRCFQZQM6CUZI · pith_short_8: QJFFRCFQ

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/QJFFRCFQZQM6CUZIMCVJNY7PI3 \
  | 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: 824a5888b0cc19e1532860aa96e3ef46e8094df2329c3e0df7fa4c04da597dad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf22a25aff697cc4303a22996ba3f7aa61a84d08a7b055ea6b3b156efa6dea08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-01-10T17:42:33Z",
    "title_canon_sha256": "f6477c62949ad14ade30f88bcebac42e3a29629fbd5889a9c3df468a428353f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2124",
    "kind": "arxiv",
    "version": 5
  }
}