Minimal Vacuum-Energy Sequestering in Closed Dust FRW Cosmology Predicts a Negative Residual Cosmological Constant

One of the greatest mysteries in modern physics is the cosmological constant problem: why is the dark energy driving the accelerated expansion of our universe so small and positive, rather than infinitely huge due to quantum vacuum fluctuations? A prominent theory known as "vacuum-energy sequestering" successfully solves the first half of this puzzle by mathematically canceling out this enormous quantum energy. However, does it predict the correct small, positive value we observe today? In this paper, we test the most minimal and predictive version of this mechanism within a universe model dominated by standard, pressureless matter (dust). We demonstrate a fundamental "no-go" result: the structural mathematical constraints of this model strictly generate a negative cosmological constant. Consequently, while minimal sequestering elegantly stabilizes the quantum vacuum, it predicts a universe that collapses rather than one that accelerates. We conclude that any successful future extension of this theory cannot simply add minor late-time fixes; it must fundamentally rethink which quantum degrees of freedom are allowed to interact with gravity. Repository Contents: This repository contains the full manuscript and the comprehensive Python codebase required to strictly reproduce all numerical and analytical claims made in the paper.