Bistability in Cellular Senescence Dynamics: Algebraic Geometry Reveals Irreversibility Thresholds in Aging

We formalize the Energy-Clearance-Senescence (E-C-S) triad of the Bio-Energetic Sequencing Model as a polynomial dynamical system with 10 kinetic parameters and 3 pharmacological controls. Under cooperative SASP feedback (quadratic senescence-energy coupling), the system exhibits bistability: a healthy equilibrium (S* approx 0.054) and a crisis equilibrium (S* approx 0.472) coexist for identical parameter values. We compute the resultant-discriminant of the steady-state ideal and prove that a saddle-node bifurcation at senolytic dosing u3 approx 0.055 eliminates the disease basin entirely. The toric structure of the zero-SASP regime yields closed-form dosing equations. Extension to the full 6D E-C-S-R-P-F system shows that all bifurcation structure is confined to the 3D core via block-triangular Jacobian reduction. These results provide the first algebraic-geometric framework for computing precise intervention thresholds in aging.