Pith Number

pith:X6IM7F2M

pith:2019:X6IM7F2MFLPQVCIZNYQAVUEUYX

not attested not anchored not stored refs pending

Endoscopy for Hecke categories, character sheaves and representations

George Lusztig, Zhiwei Yun

arxiv:1904.01176 v3 · 2019-04-02 · 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{X6IM7F2MFLPQVCIZNYQAVUEUYX}

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.

Cited by

2 papers in Pith

Relative Langlands duality and Koszul duality

Receipt and verification

First computed	2026-07-05T03:07:41.718098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf90cf974c2adf0a89196e200ad094c5f631d9c197a64af67e6118d9f142130e

Aliases

arxiv: 1904.01176 · arxiv_version: 1904.01176v3 · doi: 10.48550/arxiv.1904.01176 · pith_short_12: X6IM7F2MFLPQ · pith_short_16: X6IM7F2MFLPQVCIZ · pith_short_8: X6IM7F2M

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/X6IM7F2MFLPQVCIZNYQAVUEUYX \
  | 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: bf90cf974c2adf0a89196e200ad094c5f631d9c197a64af67e6118d9f142130e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d205503ffe99217c18fb6ca0bf315fd167a3b3c0e69cfb8e5775122f4322ee26",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2019-04-02T02:17:01Z",
    "title_canon_sha256": "980a8ea9d972a950077365cd91388a9ac7f66d4eb3a3be41c5b0fc8d13c41fa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.01176",
    "kind": "arxiv",
    "version": 3
  }
}