Pith Number

pith:43QHEQIO

pith:2009:43QHEQIODMFBXKSS4MHPSJUB5V

not attested not anchored not stored refs pending

Crystal duality and Littlewood-Richardson rule of extremal weight crystals

Jae-Hoon Kwon

arxiv:0909.1126 v2 · 2009-09-07 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{43QHEQIODMFBXKSS4MHPSJUB5V}

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	2026-05-18T04:31:51.205529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6e072410e1b0a1baa52e30ef92681ed730c6b67075102f63491a75aa49f90aa

Aliases

arxiv: 0909.1126 · arxiv_version: 0909.1126v2 · doi: 10.48550/arxiv.0909.1126 · pith_short_12: 43QHEQIODMFB · pith_short_16: 43QHEQIODMFBXKSS · pith_short_8: 43QHEQIO

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/43QHEQIODMFBXKSS4MHPSJUB5V \
  | 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: e6e072410e1b0a1baa52e30ef92681ed730c6b67075102f63491a75aa49f90aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5696ab287dd2856773657371d41037c172db14786f8708e0d2ba19250730b0e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2009-09-07T01:38:08Z",
    "title_canon_sha256": "3d7ed553f7a6ddca991cb3db6ee2865de39add96af45fa8781d6e116fd033007"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1126",
    "kind": "arxiv",
    "version": 2
  }
}