Pith Number

pith:5KBKI6ST

pith:2011:5KBKI6ST5XQOFMJAQ6RJ3YIKWP

not attested not anchored not stored refs pending

Representation type of Frobenius-Lusztig kernels

Julian K\"ulshammer

arxiv:1108.4219 v2 · 2011-08-21 · math.RT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5KBKI6ST5XQOFMJAQ6RJ3YIKWP}

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	2026-05-18T04:12:31.926675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea82a47a53ede0e2b12087a29de10ab3cc0ef247624672bfd515acaa1fa1f7db

Aliases

arxiv: 1108.4219 · arxiv_version: 1108.4219v2 · doi: 10.48550/arxiv.1108.4219 · pith_short_12: 5KBKI6ST5XQO · pith_short_16: 5KBKI6ST5XQOFMJA · pith_short_8: 5KBKI6ST

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/5KBKI6ST5XQOFMJAQ6RJ3YIKWP \
  | 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: ea82a47a53ede0e2b12087a29de10ab3cc0ef247624672bfd515acaa1fa1f7db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2103b277c6bed937a0a8dd4b7721e67f282636d1a5364cde66013b140adb28c2",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-08-21T22:30:42Z",
    "title_canon_sha256": "631434f46c711dbb7a49608f6a0ac67d938a5ed6aa36e89ad98d36382592d278"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4219",
    "kind": "arxiv",
    "version": 2
  }
}