Pith Number

pith:7YANZRNK

pith:2009:7YANZRNKJQIAYRVEWAWZ3SETPT

not attested not anchored not stored refs pending

Extensions of Simple Modules and the Converse of Schur's Lemma

Greg Marks, Markus Schmidmeier

arxiv:0903.2490 v2 · 2009-03-13 · 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{7YANZRNKJQIAYRVEWAWZ3SETPT}

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	2026-05-17T23:42:14.665264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe00dcc5aa4c100c46a4b02d9dc8937cf3255c296c29de3924fa1c77a7910a39

Aliases

arxiv: 0903.2490 · arxiv_version: 0903.2490v2 · doi: 10.48550/arxiv.0903.2490 · pith_short_12: 7YANZRNKJQIA · pith_short_16: 7YANZRNKJQIAYRVE · pith_short_8: 7YANZRNK

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/7YANZRNKJQIAYRVEWAWZ3SETPT \
  | 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: fe00dcc5aa4c100c46a4b02d9dc8937cf3255c296c29de3924fa1c77a7910a39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "622d4b20686b41f7c00b65aea21e83d2a5716e97620d770104ab9715fa114755",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2009-03-13T20:29:54Z",
    "title_canon_sha256": "998be4c57a454c884a8ae4c91545c9551310ccbbe61673988131142a1c0466c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.2490",
    "kind": "arxiv",
    "version": 2
  }
}