Pith Number

pith:SNPKYA23

pith:2019:SNPKYA23DA2LTBLSDCMLPIY4VH

not attested not anchored not stored refs pending

On the distribution of primitive subgroups of $\mathbb{Z}^{d}$ of large covolume

Michael Bersudsky

arxiv:1908.07165 v1 · 2019-08-20 · math.DS · 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{SNPKYA23DA2LTBLSDCMLPIY4VH}

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	2026-07-04T23:58:31.519215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

935eac035b1834b985721898b7a31ca9d3a66fa92f48f75210e4a00dde96fdb9

Aliases

arxiv: 1908.07165 · arxiv_version: 1908.07165v1 · doi: 10.48550/arxiv.1908.07165 · pith_short_12: SNPKYA23DA2L · pith_short_16: SNPKYA23DA2LTBLS · pith_short_8: SNPKYA23

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/SNPKYA23DA2LTBLSDCMLPIY4VH \
  | 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: 935eac035b1834b985721898b7a31ca9d3a66fa92f48f75210e4a00dde96fdb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ff364c1471379f4733cf115ef3fde0b654232ba3adb519a632f306077ff93d6",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-08-20T04:46:43Z",
    "title_canon_sha256": "a9a03611f1bc983d3e0b5bc2f6172bb19c5876f24db081b21fd2ed3538bc70a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07165",
    "kind": "arxiv",
    "version": 1
  }
}