Pith Number

pith:QK6RN4ZW

pith:2025:QK6RN4ZWYZ6DELD6GFX5CFZMWA

not attested not anchored not stored refs pending

The second moment of the size of the $2$-class group of monogenized cubic fields

Arul Shankar, Ashvin Swaminathan, Manjul Bhargava

arxiv:2506.05539 v1 · 2025-06-05 · 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{QK6RN4ZWYZ6DELD6GFX5CFZMWA}

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	2026-07-05T11:17:05.361046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82bd16f336c67c322c7e316fd1172cb00c26d97fd9f07cacf8142a80975e03fb

Aliases

arxiv: 2506.05539 · arxiv_version: 2506.05539v1 · doi: 10.48550/arxiv.2506.05539 · pith_short_12: QK6RN4ZWYZ6D · pith_short_16: QK6RN4ZWYZ6DELD6 · pith_short_8: QK6RN4ZW

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/QK6RN4ZWYZ6DELD6GFX5CFZMWA \
  | 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: 82bd16f336c67c322c7e316fd1172cb00c26d97fd9f07cacf8142a80975e03fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ed0eaf790d0766742481d0d5e17c2f63a1bdbd03d7eb0b107f4fd82f0495b3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-06-05T19:42:08Z",
    "title_canon_sha256": "47ad98fc4c8c942cbc16f7db9c5607fe5e108ec22953fa39074dc7425e8f2cf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.05539",
    "kind": "arxiv",
    "version": 1
  }
}