Pith Number

pith:QOPKIFUQ

pith:2011:QOPKIFUQTLCTQPLLFCA5QX3HD2

not attested not anchored not stored refs pending

Combinatorics of the Casselman-Shalika formula in type A

Ben Salisbury, Kyu-Hwan Lee, Philip Lombardo

arxiv:1111.1134 v2 · 2011-11-04 · math.RT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QOPKIFUQTLCTQPLLFCA5QX3HD2}

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	2026-05-18T02:53:15.748936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

839ea416909ac5383d6b2881d85f671e9bdfb8ec2bc0c028cbef77ede7baa3c5

Aliases

arxiv: 1111.1134 · arxiv_version: 1111.1134v2 · doi: 10.48550/arxiv.1111.1134 · pith_short_12: QOPKIFUQTLCT · pith_short_16: QOPKIFUQTLCTQPLL · pith_short_8: QOPKIFUQ

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/QOPKIFUQTLCTQPLLFCA5QX3HD2 \
  | 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: 839ea416909ac5383d6b2881d85f671e9bdfb8ec2bc0c028cbef77ede7baa3c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef0d20abab788254eccea00e35f34df7353248b1246aaa4a6712e7e862bfb5d0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-11-04T14:17:47Z",
    "title_canon_sha256": "e115f447940009d6c4f1f96aa1cce4168facb3059682078bffa31393852f02a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1134",
    "kind": "arxiv",
    "version": 2
  }
}