Pith Number

pith:XZ5YATA6

pith:2026:XZ5YATA6RAMD6UUVT7QWEFJ66K

not attested not anchored not stored refs resolved

Two Quantum Latin Squares of Order 6 with Cardinalities 13 and 17

Zhipeng Xu

Explicit constructions yield quantum Latin squares of order 6 with cardinalities 13 and 17.

arxiv:2605.15540 v1 · 2026-05-15 · math.CO

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\usepackage{pith}
\pithnumber{XZ5YATA6RAMD6UUVT7QWEFJ66K}

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3 Author claim open · sign in to claim

4 Citations 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

We give two explicit quantum Latin squares of order 6, one with cardinality 13 and one with cardinality 17.

C2weakest assumption

The constructions described, based on the orthogonal direct-sum decomposition of C^6 and the two-dimensional Hadamard pairs on coordinate planes, satisfy all the required properties of a quantum Latin square.

C3one line summary

Two explicit quantum Latin squares of order 6 are constructed with cardinalities 13 and 17 using direct-sum decompositions and Hadamard pairs.

References

15 extracted · 15 resolved · 5 Pith anchors

[1] Euler,Recherches sur une nouvelle espèce de quarrés magiques, Verhandelingen uit- gegeven door het Zeeuwsch Genootschap der Wetenschappen te Vlissingen9, 85–239, 1782

[2] J. Dénes and A. D. Keedwell,Latin Squares and Their Applications, Akadémiai Kiadó, Budapest, 1974 1974

[3] C. J. Colbourn and J. H. Dinitz, editors,Handbook of Combinatorial Designs, second edition, Chapman & Hall/CRC, Boca Raton, 2007 2007

[4] R. C. Bose, S. S. Shrikhande, and E. T. Parker,Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture, Canadian Journal of Mathematics12, 189–20 1960 · doi:10.4153/cjm-1960-016-5

[5] All Teleportation and Dense Coding Schemes 2001 · doi:10.1088/0305-

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:04.300424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be7b804c1e88183f52959fe162153ef29fef66d5804a015c87d7aeda2171824e

Aliases

arxiv: 2605.15540 · arxiv_version: 2605.15540v1 · doi: 10.48550/arxiv.2605.15540 · pith_short_12: XZ5YATA6RAMD · pith_short_16: XZ5YATA6RAMD6UUV · pith_short_8: XZ5YATA6

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/XZ5YATA6RAMD6UUVT7QWEFJ66K \
  | 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: be7b804c1e88183f52959fe162153ef29fef66d5804a015c87d7aeda2171824e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f68180f46b7b15eb3b0326d9f4256728d25ba9a9bedc28baa273a6ec50524bc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-15T02:24:37Z",
    "title_canon_sha256": "932fdb583257758266c583161ef3f9d169a7860c1dba995e697d857d131b3faf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15540",
    "kind": "arxiv",
    "version": 1
  }
}