Pith Number

pith:PO6CXO7G

pith:2012:PO6CXO7GQ7W4YOF2YOXNVINSLL

not attested not anchored not stored refs pending

A $(-q)$-analogue of weight multiplicities

George Lusztig, Zhiwei Yun

arxiv:1203.0521 v1 · 2012-03-02 · 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{PO6CXO7GQ7W4YOF2YOXNVINSLL}

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	2026-05-18T04:01:00.474370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bbc2bbbe687edcc38bac3aedaa1b25ad0091b9bda280ca15b8243fa2fa5ea78

Aliases

arxiv: 1203.0521 · arxiv_version: 1203.0521v1 · doi: 10.48550/arxiv.1203.0521 · pith_short_12: PO6CXO7GQ7W4 · pith_short_16: PO6CXO7GQ7W4YOF2 · pith_short_8: PO6CXO7G

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/PO6CXO7GQ7W4YOF2YOXNVINSLL \
  | 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: 7bbc2bbbe687edcc38bac3aedaa1b25ad0091b9bda280ca15b8243fa2fa5ea78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0d367a3527b266fcc30960cda348442fdc1d80556f38b468f9e59ce0a6edae8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-03-02T17:04:45Z",
    "title_canon_sha256": "858aa376436c90806d6c91b704f320879a14604661508b1cd7d1e9dc31fabc35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0521",
    "kind": "arxiv",
    "version": 1
  }
}