Earth-Like Planet around Proxima?

[Anomalocaris]

Because the luminosity of star declines exponentially with star mass,  the Goldilocks zone around a dwarve star would be in a much steeper part of the parent star's gravity well than the earth is on the sun's.   So any planet in proxima centauri's Goldilocks zone won't be earth like:   It is probably tidal locked to its parent star.  One side is perpetually day, the other perpetually night.

I believe a planet in the Goldilocks zone of most K-type stars (cool, orangish stars typically half the mass of our sun) will probably be tidally locked but there is no question about it with a red dwarf. Perhaps even more significant though, that tidal effect will have all kinds of consequences on the planet's geology. I don't know if it's inevitable that the planet would end up like Jupiter's moon, Io but would think it would have to be allot more active than Earth.

Tidal locking in itself should not make the planet more geologically active, because it circularizes the planet's orbit, and diminishes the the tidal flexing the planet under goes with each orbit.   Jupiter's inner moon is more geologically active because there are other large moons in close orbit around the planet that tugs on Io and prevent its orbit from completely circularizing.