Pith Number

pith:GZ5XYPPC

pith:2017:GZ5XYPPCLHAWLUDRQBKVBTTCUH

not attested not anchored not stored refs pending

Ringel duality as an instance of Koszul duality

Agnieszka Bodzenta, Julian K\"ulshammer

arxiv:1701.06222 v2 · 2017-01-22 · math.RT · math.AG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GZ5XYPPCLHAWLUDRQBKVBTTCUH}

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	2026-05-18T00:27:47.032463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

367b7c3de259c165d071805550ce62a1fcb95c38c45a864ad8d3885b8ef4afb9

Aliases

arxiv: 1701.06222 · arxiv_version: 1701.06222v2 · doi: 10.48550/arxiv.1701.06222 · pith_short_12: GZ5XYPPCLHAW · pith_short_16: GZ5XYPPCLHAWLUDR · pith_short_8: GZ5XYPPC

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/GZ5XYPPCLHAWLUDRQBKVBTTCUH \
  | 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: 367b7c3de259c165d071805550ce62a1fcb95c38c45a864ad8d3885b8ef4afb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5448601596fa09105218e33dde7bbb2e99f7501edfdf0b5077c7ebb70ac39a70",
    "cross_cats_sorted": [
      "math.AG",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2017-01-22T21:11:07Z",
    "title_canon_sha256": "4b2379c6c5c36af5b82dfa20b1dd4cc88aea068906c0444c4b5cf184f41bba58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.06222",
    "kind": "arxiv",
    "version": 2
  }
}