Distance-shell tomography: product kernels and sharp grid sensing
General integer-trade criterion and full-factor Cartesian-product kernel/recovery theorem; the all-order grid lower bound; and, for every n ≥ 6, the complete four-parameter integer grid kernel, exact threshold n−2 for odd n and n−3 for even n, optimal n−2 sensor count throughout 2 ≤ h < threshold, and unique four-parameter description of equal-observation populations.
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