Spacetime as Generator Readout: A Geometric Realignment of Dynamics and Kinematics from Dirac's Constraint Formalism

This paper presents a foundational refactoring of the relationship between energy-momentum and spacetime. By conducting a forensic examination of Dirac’s constraint formalism and his affine formulation of the worldline, the work establishes that spacetime is not an independent background arena. Instead, coordinate displacements are defined as the dependent, accumulated functionals of the energy-momentum generator. Key Contributions: Operational Dependency: Demonstrates that the Minkowski 4-vector encapsulates an asymmetric dependency where energy-momentum produces coordinate displacement. Action as Geometric Currency: Identifies the quantum of action ($\hbar$) as the exchange rate for spacetime, deriving intrinsic extents $\Delta t = \hbar/E$ and $\Delta x = \hbar/|p|$ from first principles. Independent Derivation of Relativity: Fully recovers Special Relativity and derives the Lorentz factor ($\gamma = E/mc^2$) as a native energy-scaling ratio rather than a kinematic correction. The Spectral Manifold ($\mathcal{K}_p$): Proposes a self-closed 4D architecture that eliminates the need for an independent 8D phase space by reducing the geometry through functional dependency. Resolution of Paradoxes: Provides geometric solutions to Pauli’s time objection, the Compton localization threshold, and the physical origin of matter waves. Empirical Falsification: The framework concludes with a precise, laboratory-accessible prediction: a quadratic ($E^2$) action-inverse temporal floor in high-energy spectral linewidths. This predicted floor ($\Gamma_{min}$) provides a clean discriminator against standard instrumental broadening $(\sqrt{E})$ and offers a direct path to empirical validation or falsification of the generator-readout geometry.