Big hypothetical question. Context: I'm in an Internet argument with someone who won't take my word for the physics; he challenged me to find someone else who would say the same thing.

1. Assume the universe runs on Newtonian mechanics. (Ignore the question of how human biochemistry works.)
2. Measure the position and velocity of every particle at some given time t.
3. Run the universe forward until a later time t1. Assume that at that time I am sitting on my porch, drinking coffee. Assume further that this condition conserves momentum and energy.
4. Restart the universe at time t, and again run forward until t1. Assume that this time, you see me jumping in the lake instead of drinking my coffee.

Question: Do these observations violate the axioms of Newtonian physics? If so, which ones?

No mention of chaos or of quantum mechanics, please: We're assuming perfect control of all variables to avoid the first one, and just handwaving away the second one.

It shouldn't be necessary, but please state your credentials.