A Completed-Theta and Modular-Epstein Reduction of the Riemann Hypothesis

We record a source-native reduction of the Riemann Hypothesis (RH) built from the completed theta representation of the Riemann xi-function. The construction begins with the full infinite theta lattice, passes through an exact two-variable correlation parent, and admits an exact lift to a determinant-one rectangular Epstein series. The Fourier transform of the tilted parent is an exact product of two completed xi-values. Differentiation returns the first two normalized generalized-Laguerre expressions and identifies the current first-rung condition, FUE-11, with a single centered determinant inequality. A separate conditional chain reduces RH to two source-specific sign assertions: an axis anchor (AX) and an all-order adjacent-rung order (LOL). The archived derivations establish LOL ⇒ RB, RB + AX ⇒ PD, and PD ⇒ RH, where RB is a reverse-barrier inequality and PD is transverse convexity of the squared completed amplitude. These implications do not establish their open premises. FUE-11 remains open; the higher-rung inequalities and AX remain open; RH is not proved. This paper organizes the exact reduction and its remaining obligations without promoting an open sign problem into a theorem. Its contribution is a structured research record. The derivations have not been independently audited here, and the manuscript is not peer reviewed.