Pith Number

pith:TQ7NUPR5

pith:2026:TQ7NUPR5MNN3LZPCGGLFKSKV5N

not attested not anchored not stored refs pending

The recording tableaux in the quantum Littlewood-Richardson map, the orthogonal transpose symmetry map, and the computation of $\mathfrak{k}$-highest weight tableaux

Olga Azenhas

A combinatorial identification proves the surjectivity of the quantum Littlewood-Richardson map on recording tableaux.

arxiv:2603.16698 v3 · 2026-03-17 · math.CO

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\usepackage{pith}
\pithnumber{TQ7NUPR5MNN3LZPCGGLFKSKV5N}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

one provides a combinatorial proof for the surjectivity of the quantum LR map which in turn exhibits the restriction of the LR orthogonal transpose symmetry map to LR-Sundaram tableaux

C2weakest assumption

That the recording tableaux produced by Watanabe's algorithm are precisely the Littlewood-Richardson-Sundaram tableaux (equinumerosity is asserted but the combinatorial identification must hold for the surjectivity argument to be complete).

C3one line summary

A combinatorial proof establishes surjectivity of the quantum LR map and yields an explicit restriction of the orthogonal transpose symmetry map to LR-Sundaram tableaux.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

The slack data of the recording tableaux in the quantum Littlewood-Richardson map determines its inverse: some applications

Receipt and verification

First computed	2026-05-26T02:05:08.459584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c3eda3e3d635bb5e5e23196554955eb7032786bf8c056180e9e2356a8020594

Aliases

arxiv: 2603.16698 · arxiv_version: 2603.16698v3 · doi: 10.48550/arxiv.2603.16698 · pith_short_12: TQ7NUPR5MNN3 · pith_short_16: TQ7NUPR5MNN3LZPC · pith_short_8: TQ7NUPR5

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/TQ7NUPR5MNN3LZPCGGLFKSKV5N \
  | 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: 9c3eda3e3d635bb5e5e23196554955eb7032786bf8c056180e9e2356a8020594

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e9a801ff39f11ad806ec49cf88d3b355756df79a303b0d5abc0b10e47baa9da",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-03-17T15:51:49Z",
    "title_canon_sha256": "4fe152df4212575c36c9d63d8f53f019f23ebce91ddb3fdca8571f7abbcbf299"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.16698",
    "kind": "arxiv",
    "version": 3
  }
}