We study a two-parameter family of infinite products A (K, d) and B (K, d), defined by quadratic rational factors with a floor-function sign alternation. Each product generates a 2×2 matrix via its coordinate grid: MA (K) is antisymmetric and MB (K) is symmetric. We prove three results. First, det MA (K) + det MB (K) = 0 for all K>0. Second, both matrices become simultaneously singular at K=1/2 (structural light cone). Third, MB (K) carries Minkowski-type indefinite signature, with det MB (1) =-1 matching the two-dimensional Minkowski metric. This geometry arises without any relativistic assumption.
Masanori Fujii (Tue,) studied this question.