Riemannian recovery does not select Lorentzian causality

Additional choices can produce Lorentzian comparators:

• with a unit one-form $\alpha$, use $g-2\alpha \otimes \alpha$;

• with an added time factor, use

  $$G=-d{T}^2+g\text{on }\mathbb{R}\times M.$$

The former introduces a direction; the latter introduces a dimension, a clock, and a product structure.

For the restricted pilot, predeclare

The map

carries the abstract pilot cone to the future cone of $G_s$. This is a verified comparator identification, not a derivation of the added time coordinate.