Six Major Open Problems as Unified Constraint System:\\ Unified Time Scale, Universe Parameter Vector \Theta\\ and Joint Solution Space

Within the standard framework of general relativity, quantum field theory and precision cosmology, six problems remain in strong tension with a naive extrapolation of known principles: the microscopic origin of black hole entropy and the information problem, the naturalness of the cosmological constant and dark energy, the structure of neutrino masses and PMNS mixing, the range of validity of the eigenstate thermalization hypothesis (ETH), the strong CP problem in QCD, and possible dispersion or Lorentz violation in gravitational waves. These are usually treated as independent questions attached to different energy scales and sectors. This work embeds all six into a single structural framework based on a unified time-scale in scattering theory, boundary time geometry and a parameterized quantum cellular automaton (QCA) / matrix universe description. A finite-dimensional parameter vector \Theta \in P \subset R^N is introduced, from which a universe object U(\Theta) is constructed. All low-energy effective constants and laws are treated as derived observables O(\Theta). The six ``open problems'' are rephrased as six scalar constraints on \Theta, forming a single constraint map $ C(\Theta) = \bigl(C_{BH},C_\Lambda,C_\nu,C_{ETH},C_{CP},C_{GW}\bigr)(\Theta) \in R^6. Technically, the construction relies on the unified time-scale identity in scattering theory, \kappa(\omega) = \varphi'(\omega){\pi} = \rho_{rel}(\omega) = 1{2\pi}\tr Q(\omega), which equates the derivative of the total scattering phase, the relative density of states and the trace of the Wigner--Smith delay operator under standard trace-class perturbation assumptions. Via a QCA/matrix-universe continuous limit, this frequency-domain time-scale controls small causal diamonds, black hole thermodynamics, the vacuum contribution to the effective cosmological constant and the propagation of long-wavelength gravitational waves. Jointly with an internal Dirac block for fermions and Yukawa textures, it also controls neutrino masses and mixing, ETH-like spectral statistics, and the effective QCD CP angle. On the mathematical side, under natural differentiability and independence hypotheses, the zero set S = \{\Theta\inP:C(\Theta)=0\} is shown to be, locally, an embedded submanifold of dimension N-6. When N=6 and the Jacobian at a physical point has full rank, the solution set is locally discrete. In addition, strong-CP and topological-sector constraints force certain components of \Theta to take values in a discrete set, so that the physically admissible parameter set is a finite or countable union of such lower-dimensional branches. This realizes, at the level of a well-defined map C(\Theta)=0, the idea that ``our Universe'' is one point (or a finite set of points) in a strongly constrained parameter space. On the physical side, the unified constraint system couples sectors that are usually analyzed separately. Black hole entropy and gravitational-wave dispersion jointly constrain the high- and low-frequency behavior of \kappa(\omega;\Theta); cosmological constant naturalness and ETH constrain the mid-frequency spectral density; neutrino mixing and strong CP link internal Dirac spectra, Yukawa phases and topological data. The framework thus yields qualitative cross-predictions between areas such as neutrino physics and cosmology, or black hole thermodynamics and gravitational-wave propagation, and defines a systematic target for model-building: construct explicit QCA/matrix-universe realizations for which the six-component constraint C(\Theta)=0$ holds.