Please forgive what I suspect is something of a rant. I'm not comfortable with the wording "strengthened GR" because there's an implicit assumption that one ca

Please forgive what I suspect is something of a rant. I'm not comfortable with the wording "strengthened GR" because there's an implicit assumption that one can straightforwardly map the authors' time-dependent parameter on the perihelion procession (their eqs (1), (2), and (3) in <https://arxiv.org/abs/2303.05567 https://arxiv.org/abs/2303.05567>) into a relativistic theory at all. The experience of various alternatives to GR (and in particular MONDian alternatives) suggests that assumption may be a bad one. What they are doing is essentially exploring a family of theories of gravitation (which may or may not solve the Einstein Field Equations, or even a comparable set of equations) where each theory in the family produces a different evolution of the orbit of a planet. General Relativity is one of the theories in that family. But how would you even get from eqns 1 & 2 with the parameter fixed at unity (and not varying in time) to the EFEs? What do the Einstein and stress-energy tensors look like? I do sympathize with the implied (and even partially-stated in §3.1) idea that each theory in the family of theories maps to a different set of initial (stress-energy) values for the planet (ignoring backreaction onto the metric) in standard GR, but I wouldn't bet much on that being right. The authors write about the (and in particular "some critical") general relativistic precession rate (or frequency), and I don't mind that wording.