The Time Dilation Network (TDN) v2: Core Framework and Open Problems

Version 2 of the Time Dilation Network (TDN) framework. It supersedes neither the original record (Version 1, DOI 10.5281/zenodo.20625572) nor the numerical study (DOI 10.5281/zenodo.20684044), but reorganizes the framework in light of both. This version sorts all claims into three layers by epistemic status. Surviving core: the definition of time as longest causal chain, tau = alpha L_max, and results that follow directly from the model's definitions, including the internal Page-curve consistency theorem under stated assumptions. Falsified or withdrawn: a sharp second-order phase transition at rho_c, a universal scaling exponent, ensemble-independent scaling, and all cosmological inferences that depended on them. The uniform-sampling model is identified as the known Barak-Erdos graph; this identifies the sampling, not the full action-weighted framework, whose equivalence to known models remains open. Open problems: reconstruction of a Lorentzian manifold, existence of a physical generator, why the longest chain (rather than another causal functional) should be the physical time, and whether any dynamics selects an ensemble yielding effective dimension d=4 without assuming it. The word Theorem is used only where a proof exists within the model's definitions. TDN v2 is presented as a framework for defining time on causal networks together with an explicit research program, not as a complete theory of emergent spacetime, and not as a contribution proven independent of causal set theory.