Pith Number

pith:XOECWN2I

pith:2009:XOECWN2IXAOTM7SP4FLZCVH5XW

not attested not anchored not stored refs pending

Langlands duality for representations and quantum groups at a root of unity

Kevin McGerty

arxiv:0902.1485 v3 · 2009-02-09 · math.QA · 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{XOECWN2IXAOTM7SP4FLZCVH5XW}

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	2026-05-18T02:14:48.661313Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb882b3748b81d367e4fe1579154fdbd87f96573716d4f7d21685db0a62eabef

Aliases

arxiv: 0902.1485 · arxiv_version: 0902.1485v3 · doi: 10.48550/arxiv.0902.1485 · pith_short_12: XOECWN2IXAOT · pith_short_16: XOECWN2IXAOTM7SP · pith_short_8: XOECWN2I

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/XOECWN2IXAOTM7SP4FLZCVH5XW \
  | 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: bb882b3748b81d367e4fe1579154fdbd87f96573716d4f7d21685db0a62eabef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d7f6e445d216b7fabb041b318098530e517ad5c8823a58fa3f7bc3424af11cc",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2009-02-09T17:52:53Z",
    "title_canon_sha256": "f164d6bbcdc551812adc3254cdfae361170f3bfef5d151d7b49f4994ce123268"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1485",
    "kind": "arxiv",
    "version": 3
  }
}