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Hadamard configurations and sharp cubic-period bounds for stealth in dimensions 10, 11, and 12 — arXiv:2611.06148

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.06148
License (as archived): CC0-1.0
Archived: 2026-11-05T18:27:54.511Z
SHA-256 of the archived text: 95ba4f34a7df9af854ee1f19724d023662c1fd44eb7199fc916e92bbe46ade54
Stable URL of this page: https://metraipolis.com/documento/dc_9eddcb89367d

How to cite

Hadamard configurations and sharp cubic-period bounds for stealth in dimensions 10, 11, and 12 — arXiv:2611.06148 — arXiv (en), https://arxiv.org/abs/2611.06148 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_9eddcb89367d (Metraipolis archive dc_9eddcb89367d, sha256 95ba4f34a7df9af854ee1f19724d023662c1fd44eb7199fc916e92bbe46ade54)

BibTeX

@misc{dc9eddcb89367d,
  title = {Hadamard configurations and sharp cubic-period bounds for stealth in dimensions 10, 11, and 12 — arXiv:2611.06148},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.06148},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_9eddcb89367d; sha256 95ba4f34a7df9af854ee1f19724d023662c1fd44eb7199fc916e92bbe46ade54},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.06148. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We construct explicit, nonlattice periodic point configurations in dimensions $10$, $11$ and $12$ with stealth center density $1/24$ and unit-density stealth radius $2\cdot24^{-1/n}$. These values exceed those of duals of the current record lattice packings, without claiming to exceed all possible lattices. The construction uses the $24$ sign rows of an order-$12$ Hadamard matrix and their antipodes, projected onto $n$ coordinates. For an arbitrary, not necessarily binary, equally weighted motif with marked period $2\mathbb{Z}^n$, we prove a sharp $2n$-point lower bound for a raw stealth radius at least one and classify equality by antipodal Hadamard configurations. We deduce bounded-complexity optimality, sharp optimality among binary motifs in dimensions $10$--$12$, and local maximality under simultaneous perturbations of the motif and the marked period shape. A divisibility argument excludes ordinary equally weighted periodic formal duals. Statements are confined to their indicated classes; no global optimality among arbitrary-period configurations is asserted.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Metric Geometry (math.MG) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2611.06148 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-05T18:18:04.075Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).