Pith Number

pith:WSGZBZ2K

pith:2017:WSGZBZ2KNEZG3B75ZY6ECD25GO

not attested not anchored not stored refs pending

The average sizes of two-torsion subgroups in quotients of class groups of cubic fields

Zev Klagsbrun

arxiv:1701.02838 v3 · 2017-01-11 · 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{WSGZBZ2KNEZG3B75ZY6ECD25GO}

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	2026-05-18T00:34:57.619897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b48d90e74a69326d87fdce3c410f5d33996bd924d1cfe09f329dc045affe0d4d

Aliases

arxiv: 1701.02838 · arxiv_version: 1701.02838v3 · doi: 10.48550/arxiv.1701.02838 · pith_short_12: WSGZBZ2KNEZG · pith_short_16: WSGZBZ2KNEZG3B75 · pith_short_8: WSGZBZ2K

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/WSGZBZ2KNEZG3B75ZY6ECD25GO \
  | 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: b48d90e74a69326d87fdce3c410f5d33996bd924d1cfe09f329dc045affe0d4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29da2da92ac40030ba0fe234b66d5f4c11da8d3ff4b36500f946ed71e035b010",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-01-11T03:23:54Z",
    "title_canon_sha256": "745634fba664d3ba49ee41f81372e8446a372e07ce63506c97cc1b46aaeef7e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.02838",
    "kind": "arxiv",
    "version": 3
  }
}