Pith Number

pith:TYQZKLT4

pith:2020:TYQZKLT4C2EJP7IQ5GCHXGL4GW

not attested not anchored not stored refs pending

The mean number of 2-torsion elements in the class groups of $n$-monogenized cubic fields

Arul Shankar, Jonathan Hanke, Manjul Bhargava

arxiv:2010.15744 v1 · 2020-10-29 · 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{TYQZKLT4C2EJP7IQ5GCHXGL4GW}

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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.

Cited by

1 paper in Pith

A parametrization of $3$-class groups of quadratic rings over Dedekind domains

Receipt and verification

First computed	2026-07-05T01:47:40.126483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e21952e7c168897fd10e9847b997c359daa85fda7e87cf7e61f0ee4d22b8769

Aliases

arxiv: 2010.15744 · arxiv_version: 2010.15744v1 · doi: 10.48550/arxiv.2010.15744 · pith_short_12: TYQZKLT4C2EJ · pith_short_16: TYQZKLT4C2EJP7IQ · pith_short_8: TYQZKLT4

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/TYQZKLT4C2EJP7IQ5GCHXGL4GW \
  | 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: 9e21952e7c168897fd10e9847b997c359daa85fda7e87cf7e61f0ee4d22b8769

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a9a680798bc4fe0f99ccb9ec1d40cba7372cc208731f2f4bb79e466fe51d8ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-10-29T16:45:21Z",
    "title_canon_sha256": "11eb282280354e64ddef610ab099f2e8a74b4463c8189e89f96556d676317b92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.15744",
    "kind": "arxiv",
    "version": 1
  }
}