Minkowski-Type Geometry from Block-Alternating Infinite Products

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: M_A(K) is antisymmetric and M_B(K) is symmetric. We prove three results. First, det M_A(K) + det M_B(K) = 0 for all K>0. Second, both matrices become simultaneously singular at K=1/2 (structural light cone). Third, M_B(K) carries Minkowski-type indefinite signature, with det M_B(1)=-1 matching the two-dimensional Minkowski metric. This geometry arises without any relativistic assumption.