Pith Number

pith:KKPZM4ZW

pith:2010:KKPZM4ZWPXUC5PDW43R6JWPODB

not attested not anchored not stored refs pending

Affine crystals, one-dimensional sums and parabolic Lusztig q-analogues

Cedric Lecouvey, Mark Shimozono, Masato Okado

arxiv:1002.3715 v2 · 2010-02-19 · math.QA · 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{KKPZM4ZWPXUC5PDW43R6JWPODB}

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	2026-05-18T04:22:40.431068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

529f9673367de82ebc76e6e3e4d9ee1841555302185e421a5a1496eac2e89d41

Aliases

arxiv: 1002.3715 · arxiv_version: 1002.3715v2 · doi: 10.48550/arxiv.1002.3715 · pith_short_12: KKPZM4ZWPXUC · pith_short_16: KKPZM4ZWPXUC5PDW · pith_short_8: KKPZM4ZW

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/KKPZM4ZWPXUC5PDW43R6JWPODB \
  | 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: 529f9673367de82ebc76e6e3e4d9ee1841555302185e421a5a1496eac2e89d41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d20b4ed81b4fbfb65892ca5d8c6f37acf2331e8f34af24e52e98b658a670c7aa",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-02-19T11:19:39Z",
    "title_canon_sha256": "1f95a6a47b256b65822d4dd160c81451a69d6d9dc7841e3c4ce8fee95f49bd8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.3715",
    "kind": "arxiv",
    "version": 2
  }
}