The 5-Integrality of the Four-Loop Equal-Mass Banana Integral

The ε-factorized differential equation of the four-loop equal-mass banana integral is conjectured to be free of the prime 5 at every order in the dimensional regularization parameter. I study the first leg of this conjecture as a statement about a tower of power series under the operator U₅ and prove a reduction theorem. The full tower of congruences follows from three inputs that are proved or verified exactly, together with a single growth statement about one explicitly computed series. I prove that the tower is stationary modulo 5 at an explicit rational fixed point, establish a two-layer expansion with 5-adic slopes 1 and 3, and locate the exact digit at which rational structure ends. Every identity is verified on 15,614 exact coefficients. The de Rham Frobenius of the underlying Calabi-Yau operator, recomputed exactly through order z⁶⁰⁰, is polynomial digit by digit with sharp break points, a finite-support staircase. The one question that remains open is a measurable number, and I state precisely what value decides it.