Pith Number

pith:2OGI7H2Q

pith:2017:2OGI7H2QFNVG5GKUBPBAKQ2EOC

not attested not anchored not stored refs pending

How many units can a commutative ring have?

Keir Lockridge, Sunil K. Chebolu

arxiv:1701.02341 v1 · 2017-01-09 · math.AC · math.GR · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2OGI7H2QFNVG5GKUBPBAKQ2EOC}

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	2026-05-18T00:53:04.500698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d38c8f9f502b6a6e99540bc205434470960243b2402b6ec01307e963ddebdfc5

Aliases

arxiv: 1701.02341 · arxiv_version: 1701.02341v1 · doi: 10.48550/arxiv.1701.02341 · pith_short_12: 2OGI7H2QFNVG · pith_short_16: 2OGI7H2QFNVG5GKU · pith_short_8: 2OGI7H2Q

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/2OGI7H2QFNVG5GKUBPBAKQ2EOC \
  | 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: d38c8f9f502b6a6e99540bc205434470960243b2402b6ec01307e963ddebdfc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f725075e59a15e5463119752a19491746f45616951753c4877939816024f641",
    "cross_cats_sorted": [
      "math.GR",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-01-09T20:32:31Z",
    "title_canon_sha256": "0187025107261dcc15e924682795212b9265e15f2329044ca302a8256ec99c18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.02341",
    "kind": "arxiv",
    "version": 1
  }
}