This paper replaces my earlier manuscript, Recovering Relativity from Temporal Continuity. That paper carried the right continuity first architecture, but it treated exact derivations, structural selections, physical projections and future research targets too nearly as one level of result. Version 2.0 retains the full programme rather than reducing it to one narrow relativity paper, while repairing every bridge that previously outran its mathematics. I begin with a parent temporal continuity law and derive the conserved four current under explicit compactification, regularity and zero net fibre exchange conditions. Invariant current density is then separated from the density and drift measured by a declared timelike frame. On a positive barotropic and irrotational ideal branch, the closed evolution has a stable inverse over every attained smooth interval carrying complete compatible state and boundary data. This is the first recoverability result. It is a state reconstruction theorem for the branch actually reached by the evolution. It does not extend through shocks, density zeros, unrecorded boundary exchange or undeclared dissipation. The relativistic reconstruction is then separated into distinct steps. A finite isotropic principal speed supplies an invariant signal cone. Linearity, homogeneity, isotropy, reciprocity and preservation of that cone select the Lorentz comparison group. Continuity does not supply those assumptions by itself. The normalised quadratic response of the closed scalar branch defines a symmetric densitised inverse tensor. In four dimensions its determinant fixes the volume factor, and the complete effective metric is recovered. The result goes beyond reconstruction of a conformal cone alone. The recovered metric remains the effective metric seen by that perturbation branch. It is not identified with the universal gravitational metric without additional stress, Bianchi, coupling and observational validation. Metric compatibility and vanishing torsion then select the Levi-Civita connection. Locality, covariance, symmetry, four dimensionality, second order metric dependence and divergence compatibility separately select the Einstein tensor with a possible cosmological term as the large scale metric closure form. This is a Lovelock selection result. It is not a derivation of the gravitational coupling, the matter source or the microscopic origin of spacetime from continuity alone. The wider sectors are retained and repaired. Recoverability is no longer represented by an undefined ratio of accessible to total information. It is defined through a branch-specific observation map acting on a physical quotient state space. Injectivity gives formal recovery. The smallest singular value and propagated covariance determine whether that recovery is stable enough to be useful. Persistence records the interval over which the same admissible and recoverable branch remains valid. Thermodynamic coarse graining is treated as a declared stochastic map that contracts distinguishability. Quantum continuity is derived for a declared Hamiltonian, while decoherence is treated through quantum channels and recovery maps. Horizons are represented as observer-dependent restrictions of the accessible algebra or domain rather than as the same physical process as decoherence. Cosmological inference is written as a finite past light cone observation map rather than an integral over an undefined total universe. The graphene Dirac fluid remains the empirical anchor. Joint charge and heat transport provide an invertible map for the intrinsic conductivity, enthalpy density and momentum relaxation time on the homogeneous hydrodynamic branch. The neutral collective mode also carries its own effective signal metric. This condensed matter metric is not promoted to the gravitational metric. The paper corrects the earlier closure residual construction as well. A Lorentzian contraction is not a positive norm. I replace it with an observer-resolved positive decomposition and require any proposed residual relaxation law to follow from an independently supplied evolution equation. Every retained sector is classified as an exact theorem, a selection result, a conditional projection or an open promotion gate. A final status table records what has been recovered, what assumptions were added and what remains unresolved. The release contains the complete manuscript, eight editable vector figures, the full improvement ledger, a pre-submission checklist and checksums for every publication file. Version 2.0 supersedes the earlier manuscript as the active mathematical authority for the continuity first recovery of relativity and its cross-regime recoverability programme.
Roy Herbert (2026) studied this question.