local weight_of_platform_foundation_tiles = 200
local shape_constant = 0.8862 -- (pi/4)^0.5. This value means that circular platforms are unaffected. A shape_constant of 1 would mean square platforms are unaffected.

local replacement_for_width = "(weight / ("
.. weight_of_platform_foundation_tiles
.. " * "
.. shape_constant
.. ")) ^ 0.5"

shape_constant has redundant square roots (or it is in the wrong bracket level)

fix:
local replacement_for_width = "(weight / "
.. weight_of_platform_foundation_tiles
.. ") ^ 0.5 * "
.. shape_constant

Yup, the square root was applied twice.

You seem to have inverted the definition of shape_constant in your suggestion, but apart from that it is correct.

Thanks for the report.

Thank you for your fix.