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

Abstract

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.