Minimum ratios from overlapping aggregate disclosures: a constructive finite-history model

This technical note studies minimum monthly ratios from exact aggregate disclosures on a fixed calendar of 21 months. Four windows of length 12, shifted by three months, give the arithmetic means of positive denominators D, nonnegative numerators H, and ratios R=H/D. An explicit three-month realization criterion reduces compatibility of the shared history to nine variables. The possible terminal minima form [0,U] or [0,U), with zero attained and endpoint membership determined by strict feasibility. Eight overlap bounds give U<=U_R for general compatible inputs. In the proportional disclosure class d_k=d_0>0, h_k=d_0 r_k and r_k>=0, compatibility is equivalent to U_R>=0 and the sharp range is [0,U_R]. Analytic examples give [0,2] for the last window alone versus [0,4/5] under all four windows, and an unattained supremum with range [0,1). Version v1 is designated as the first public technical-note release.