Pith Number

pith:LP4XU54B

pith:2016:LP4XU54BTXIMVKGJHOFLOT2EZC

not attested not anchored not stored refs pending

The elementary 3-Kronecker modules

Claus Michael Ringel

arxiv:1612.09141 v1 · 2016-12-29 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LP4XU54BTXIMVKGJHOFLOT2EZC}

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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.

Cited by

1 paper in Pith

Claus Michael Ringel's main contributions to Gorenstein-projective modules

Receipt and verification

First computed	2026-05-18T00:53:46.377921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bf97a77819dd0caa8c93b8ab74f44c8bc92a5bb90b26f3f564922d9f7b2a4ce

Aliases

arxiv: 1612.09141 · arxiv_version: 1612.09141v1 · doi: 10.48550/arxiv.1612.09141 · pith_short_12: LP4XU54BTXIM · pith_short_16: LP4XU54BTXIMVKGJ · pith_short_8: LP4XU54B

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/LP4XU54BTXIMVKGJHOFLOT2EZC \
  | 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: 5bf97a77819dd0caa8c93b8ab74f44c8bc92a5bb90b26f3f564922d9f7b2a4ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d098f5846f017ed010647bc11749340b3d764ddf4c94dbc3f1a79af7ef2ed8ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2016-12-29T13:46:39Z",
    "title_canon_sha256": "d0c547c06c3290722eedb2b72d92feef71b52b2cf25a08ef85ae2e8d58146939"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09141",
    "kind": "arxiv",
    "version": 1
  }
}