Minimal support cardinality S_d(N) of nontrivial origin-nonzero Dirichlet solutions is nondecreasing in d, so S_4(N) ≳ N²/log N, matching even-dimensional constructions up to a log factor.
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On Support Cardinality for the Discrete Schr\"odinger Equation
Minimal support cardinality S_d(N) of nontrivial origin-nonzero Dirichlet solutions is nondecreasing in d, so S_4(N) ≳ N²/log N, matching even-dimensional constructions up to a log factor.