In Wolfram’s and Gorard’s papers ([2004.08210] A Class of Models with the Potential to Represent Fundamental Physics and [2004.14810] Some Relativistic and Gravitational Properties of the Wolfram Model), the claim seems to be that Lorentz symmetry/invariance/covariance automatically follows from causal invariance.
However, what they mean with Lorentz symmetry seems to refer to a much weaker property, since there is no Lorentz group O(1,3) appearing in their paper. Regarding special relativity, If there is no true Lorentz symmetry from Wolfram models, then is there any real improvement over the pre-existing causal set theory?