The evolutionary path of the Sun has been described in some detail, and, subtle differences aside, it's been described as such for decades - the Earth-engulfing red giant stage, the helium flash, etc.. It would seem that the knowledge necessary to make such a prediction has been around since the 60s, if not earlier.
How do we know it will happen, and on the timescales described? If we make some measurements/estimations of the mass and composition of the Sun, and use our understanding of nuclear physics - energy of fusion and so forth, and an understanding of Newtonian physics (or do we have to invoke Einstein?), do the predictions just inevitably fall out?
Could the predictions be wrong? Is there any significant measure of uncertainty, perhaps due to sensitivity of certain calculations to initial conditions, etc?
Is the red giant future of our Sun a firm conclusion, or just a likely possibility among a range of others and commonly talked about merely because it seems the most likely one?