The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry… - Hans Reichenbach

If the definition of simultaneity is given from a moving system, the spherical surface will result when Einstein's definition with є = 1/2 is used, since it is this definition which makes the velocity of light equal in all directions.

Although it is admitted that certain differences cannot be verified by experiment, we should not infer from this fact that they do not exist. ...we are accused of having confused subjective inability with objective indeterminacy.

Light signals alone provide the metrical structure of the four-dimensional space-time continuum. The construction may be called light axioms.