Pith Number

pith:5W55EGUL

pith:2014:5W55EGULYC3Z27ZN56TAS2J7G6

not attested not anchored not stored refs pending

The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders

Ila Varma, Manjul Bhargava

arxiv:1401.5875 v1 · 2014-01-23 · 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{5W55EGULYC3Z27ZN56TAS2J7G6}

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	2026-05-18T03:01:23.521776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edbbd21a8bc0b79d7f2defa609693f379bf2c966fb19be5a41eaa132a9391818

Aliases

arxiv: 1401.5875 · arxiv_version: 1401.5875v1 · doi: 10.48550/arxiv.1401.5875 · pith_short_12: 5W55EGULYC3Z · pith_short_16: 5W55EGULYC3Z27ZN · pith_short_8: 5W55EGUL

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/5W55EGULYC3Z27ZN56TAS2J7G6 \
  | 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: edbbd21a8bc0b79d7f2defa609693f379bf2c966fb19be5a41eaa132a9391818

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b262e14ef8a3754acee758e63b3a2b1ca76255d31250f3b6cf5eb6ffae61856",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-01-23T05:22:11Z",
    "title_canon_sha256": "bef48f1abf9f176afca0aef007b527229b67893569a55c8ef07abd3584977b0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.5875",
    "kind": "arxiv",
    "version": 1
  }
}