Pith Number

pith:3QKHDP7W

pith:2017:3QKHDP7W63FUFS2AENJXISOHIA

not attested not anchored not stored refs pending

Class numbers and $p$-ranks in ${\mathbb Z}_p^d$-towers

Daqing Wan

arxiv:1712.02906 v3 · 2017-12-08 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3QKHDP7W63FUFS2AENJXISOHIA}

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	2026-05-18T00:14:48.217394Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc1471bff6f6cb42cb4023537449c74004a2b775bf367024a0b2d502bf3ad944

Aliases

arxiv: 1712.02906 · arxiv_version: 1712.02906v3 · doi: 10.48550/arxiv.1712.02906 · pith_short_12: 3QKHDP7W63FU · pith_short_16: 3QKHDP7W63FUFS2A · pith_short_8: 3QKHDP7W

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/3QKHDP7W63FUFS2AENJXISOHIA \
  | 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: dc1471bff6f6cb42cb4023537449c74004a2b775bf367024a0b2d502bf3ad944

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "299f322f8b239366a6a5d3efa098f390ae44218a18460fe3f4c5618e528a6e98",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-12-08T01:20:15Z",
    "title_canon_sha256": "84fedd2a19224b7855bb2583abfde88d0d72b4f304c71c7b30c42fd380615dc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.02906",
    "kind": "arxiv",
    "version": 3
  }
}