Pith Number

pith:QH67ALOB

pith:2011:QH67ALOBGBOES5PVUAZPOVMDZL

not attested not anchored not stored refs pending

Koszul duality and semisimplicity of Frobenius

Pramod N. Achar, Simon Riche

arxiv:1102.2820 v1 · 2011-02-14 · math.RT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QH67ALOBGBOES5PVUAZPOVMDZL}

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	2026-05-18T04:28:46.342147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81fdf02dc1305c4975f5a032f75583caf07c909b162340cc9e9dbe0ef9c1ba53

Aliases

arxiv: 1102.2820 · arxiv_version: 1102.2820v1 · doi: 10.48550/arxiv.1102.2820 · pith_short_12: QH67ALOBGBOE · pith_short_16: QH67ALOBGBOES5PV · pith_short_8: QH67ALOB

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/QH67ALOBGBOES5PVUAZPOVMDZL \
  | 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: 81fdf02dc1305c4975f5a032f75583caf07c909b162340cc9e9dbe0ef9c1ba53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "762317328b6a84e72a5dc9ff8b6a49b79fc60b379916ae89953bc651dad731a3",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-02-14T16:27:27Z",
    "title_canon_sha256": "45ff1f147170a93636ddf69fdcd9df3eae4b45f3920aff6301ed1c8b83d11bd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2820",
    "kind": "arxiv",
    "version": 1
  }
}