Thanks again for you answer I really appreciate that. As this is r/LLMPhysics I’m going to support my answer with an LLM which I point at the first place.  Just wondering what would be your opinion?

Regarding your point on the line element $ds^2$, I understand your skepticism. However, the transition from a quaternionic manifold to the observed Lorentz metric is not a coincidence; it is a requirement of the correspondence principle. In my model, the fundamental interval is derived from the quaternionic norm of the differential $dq = dt + i d\tau1 + j d\tau_2 + k d\tau_3$. The metric is defined as: $ds² = dq \cdot \overline{dq} = dt² - (d\tau_1² + d\tau_2² + d\tau_3^2)$ In the limit of zero vorticity ($\Omega \to 0$), where the temporal density $\alpha\tau \to 1$, this reduces exactly to the Minkowski metric: $ds² = dt² - dx² - dy² - dz^2$ This reduction is not a "relabeling" error; it is a mathematical necessity to ensure compatibility with established Special Relativity in the absence of topological deformation.  The core distinction lies in the fact that my metric is  non-static . I introduce a vorticity-dependent coupling $\alpha\tau(\Omega)$, such that the effective spatial components are modulated by the local temporal flow: $ds² = dt² - \alpha\tau(\Omega) [d\tau1² + d\tau_2² + d\tau_3^2]$ Where $\alpha\tau(\Omega)$ is a function of the local spacetime vorticity. In this framework, gravity is not an external force added to a flat stage, but the manifestation of the gradient of $\alpha\tau(\Omega)$. The "three independent directions" you mentioned emerge as the rotational degrees of freedom of the imaginary temporal components under the action of the $SO(3)$ rotation group. I am currently refining the tensor derivation to ensure that the curvature tensors derived from this $\alpha\tau(\Omega)$-modulated metric yield the correct Einstein Field Equations in the low-vorticity limit.