If I change Cm0, I change the trim requirement. i.e. CLt.
I do not change CL.
I therefore change the CL:CLt ratio.
But a Cm0 shift does not change the stability (or lack thereof) in any way.
Therefore there is no causal relationship between CL:CLt and stability.
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A practical aircraft has a pitching moment when the wing/body generates no lift. Therefore a tail lift term is required for trim at CL(wing)=0
If the proportionality argument held water, it would be absolutely impossible to hold a stable condition here, because any change in wing lift is infinite as a proportion, while the corresponding tail lift proportional change is finite.
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Fundamentally, the Lw*a=Lt*b relation is a gross over-simplification - as I mentioned before, that's not the way it's done to actually determine stability, because of issues like Cm0.