Pith Number

pith:XCFR7INQ

pith:2009:XCFR7INQZFA7E7K6GMD7OM32VN

not attested not anchored not stored refs pending

Simple group graded rings and maximal commutativity

Johan \"Oinert

arxiv:0904.4661 v1 · 2009-04-29 · 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{XCFR7INQZFA7E7K6GMD7OM32VN}

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	2026-07-04T15:41:56.612748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b88b1fa1b0c941f27d5e3307f7337aab5b05d816768da8636f400827e65f5e3b

Aliases

arxiv: 0904.4661 · arxiv_version: 0904.4661v1 · doi: 10.48550/arxiv.0904.4661 · pith_short_12: XCFR7INQZFA7 · pith_short_16: XCFR7INQZFA7E7K6 · pith_short_8: XCFR7INQ

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/XCFR7INQZFA7E7K6GMD7OM32VN \
  | 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: b88b1fa1b0c941f27d5e3307f7337aab5b05d816768da8636f400827e65f5e3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faab6253a9de816cd8105129473bd921706c29bd87c14c1f88cc6c96fa6e0985",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2009-04-29T16:47:41Z",
    "title_canon_sha256": "68f7d1a58681bdc90d6a9dd2adf83d76c5715c365c8b656ee6631b737664e74e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.4661",
    "kind": "arxiv",
    "version": 1
  }
}