Pith Number

pith:GBKFQBAD

pith:2012:GBKFQBADMDJDSEUGU7XZ2HWCM6

not attested not anchored not stored refs pending

On rings each of whose finitely generated modules is a direct sum of cyclic modules

Gholamreza Behboodi Eskandari, Mahmood Behboodi

arxiv:1202.0386 v2 · 2012-02-02 · math.RA · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GBKFQBADMDJDSEUGU7XZ2HWCM6}

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	2026-05-18T03:43:18.452912Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

305458040360d2391286a7ef9d1ec26796fde45321c8b7b33633a07f1c6c3a0e

Aliases

arxiv: 1202.0386 · arxiv_version: 1202.0386v2 · doi: 10.48550/arxiv.1202.0386 · pith_short_12: GBKFQBADMDJD · pith_short_16: GBKFQBADMDJDSEUG · pith_short_8: GBKFQBAD

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/GBKFQBADMDJDSEUGU7XZ2HWCM6 \
  | 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: 305458040360d2391286a7ef9d1ec26796fde45321c8b7b33633a07f1c6c3a0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2431d21eda8f7b4dadbbfb96a5848038c61158969bb50297fb38ca876ac870dd",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-02-02T09:01:31Z",
    "title_canon_sha256": "933964fff036c1d0d9a952f115116852a1d3f2f388eccfed2b3e19059f2c5c26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.0386",
    "kind": "arxiv",
    "version": 2
  }
}