[Retric]

Calling it a valid paradox is questionable, there’s a little mathematical sleight of hand required for the particle to actually stop in finite time. It doesn’t work for say particle sliding up a sphere.

To work the curvature of the dome is infinite is at the apex, which then breaks many things. There’s a lot of disagreements around this paradox and much older related examples because Newtonian physics is somewhat ill defined: https://philsci-archive.pitt.edu/8833/1/dome_v3.pdf

[ASalazarMX]

Since many thought experiments allow for objects to be composed of infinite one-dimensional points that somehow form higher-dimensional bodies, an infinite curvature could be interpreted as the apex being a single point supporting the point at the bottom of the ball. Both points should be perfectly aligned and in perfect equilibrium.

It has no reason to roll unless the placement was uneven, and if it was uneven, it would not break determinism.