Pith Number

pith:EYWIWKXX

pith:2010:EYWIWKXXGAIO2EGSRFVL7AR4AY

not attested not anchored not stored refs pending

Counting Subrings of ${\mathbb Z}^n$ of finite index

Jake Marcinek, Nathan Kaplan, Ramin Takloo-Bighash

arxiv:1008.2053 v3 · 2010-08-12 · 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{EYWIWKXXGAIO2EGSRFVL7AR4AY}

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	2026-05-18T02:45:41.366683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

262c8b2af73010ed10d2896abf823c063a33a6e1987db01df4df345ba4e04fcc

Aliases

arxiv: 1008.2053 · arxiv_version: 1008.2053v3 · doi: 10.48550/arxiv.1008.2053 · pith_short_12: EYWIWKXXGAIO · pith_short_16: EYWIWKXXGAIO2EGS · pith_short_8: EYWIWKXX

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/EYWIWKXXGAIO2EGSRFVL7AR4AY \
  | 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: 262c8b2af73010ed10d2896abf823c063a33a6e1987db01df4df345ba4e04fcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40f3fe4829c8539e65d2f64da6558adf1582f8e7222d72ad91d7bb9000206c76",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-08-12T06:32:55Z",
    "title_canon_sha256": "c99851b24ec78617b6e6654584dd0b4fb8e7b432c93a763407286ba840765692"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.2053",
    "kind": "arxiv",
    "version": 3
  }
}