Pith Number

pith:EAZBTXER

pith:2026:EAZBTXEROVX6YN4KDJM3CSQIXP

not attested not anchored not stored refs resolved

Hadamard Hypercubes

Amin Bahmanian, Sho Suda

Two constructions produce Hadamard hypercubes from conference matrices and from recursive merges with Latin hypercubes.

arxiv:2605.16722 v1 · 2026-05-16 · math.CO

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Claims

C1strongest claim

We introduce two constructions of Hadamard hypercubes. The first construction is derived from conference matrices, while the second is recursive, combining Hadamard matrices (and hypercubes) of smaller order with Latin hypercubes.

C2weakest assumption

The defined Hadamard hypercubes satisfy the required higher-dimensional orthogonality or balance conditions, and the recursive combination with Latin hypercubes preserves these properties without introducing inconsistencies in the multi-dimensional setting.

C3one line summary

The authors present two constructions of Hadamard hypercubes: one derived from conference matrices using association schemes on triples, and a recursive construction combining smaller Hadamard matrices or hypercubes with Latin hypercubes, yielding applications to higher-dimensional symmetric designs

References

46 extracted · 46 resolved · 1 Pith anchors

[1] Symmetric layer-rainbow colorations of cubes.SIAM J 2023

[2] A review and new symmetric conference matrices.University of Wollongong 2014

[3] Benjamin/Cummings Publishing Company, California, 1984 1984

[4] The edge-coloring of complete hypergraphs 1979

[5] Brouwer and Willem H 2012

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:38.430628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

203219dc91756fec378a1a59b14a08bbfd1f01045828d4005fff2d53f37f23b4

Aliases

arxiv: 2605.16722 · arxiv_version: 2605.16722v1 · doi: 10.48550/arxiv.2605.16722 · pith_short_12: EAZBTXEROVX6 · pith_short_16: EAZBTXEROVX6YN4K · pith_short_8: EAZBTXER

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EAZBTXEROVX6YN4KDJM3CSQIXP \
  | 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: 203219dc91756fec378a1a59b14a08bbfd1f01045828d4005fff2d53f37f23b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61afcb9a369f3d53371dd4b7a304b02c91be1862abcce4d0ce3d5a860b4037fa",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-16T00:11:19Z",
    "title_canon_sha256": "47360971c3ee2af69f5611ac329674890adfbf08602bfd4c5258b5d1d9d61fb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16722",
    "kind": "arxiv",
    "version": 1
  }
}