Pith Number

pith:MPCRVP74

pith:2016:MPCRVP747MLSEI4GUJVMFSGF3O

not attested not anchored not stored refs pending

Counting Finite Index Subrings of $\mathbb{Z}^n$

Benjamin Krakoff, Julia Menzel, Nathan Kaplan, Stanislav Atanasov

arxiv:1609.06433 v5 · 2016-09-21 · math.CO · 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{MPCRVP747MLSEI4GUJVMFSGF3O}

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	2026-07-05T03:50:45.122859Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63c51abffcfb17222386a26ac2c8c5dba49d00f8443f64e3275d6596f786d926

Aliases

arxiv: 1609.06433 · arxiv_version: 1609.06433v5 · doi: 10.48550/arxiv.1609.06433 · pith_short_12: MPCRVP747MLS · pith_short_16: MPCRVP747MLSEI4G · pith_short_8: MPCRVP74

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/MPCRVP747MLSEI4GUJVMFSGF3O \
  | 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: 63c51abffcfb17222386a26ac2c8c5dba49d00f8443f64e3275d6596f786d926

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59f110a13a5a5ad442f35707c36a8ded5b153d2b22b2bfe1d3afb9dce60b8a79",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-21T06:47:11Z",
    "title_canon_sha256": "d1c0626200b80133b1acac214f8ee45a9579e1c47f51e5ac6ffc30a87b722c78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06433",
    "kind": "arxiv",
    "version": 5
  }
}