Quantum Theory from Grand Consistency Theory

This paper develops the quantum sector of Grand Consistency Theory (GCT) from its underlying microscopic constraint structure. Starting from emergent Lorentzian spacetime and the Constraint Laplacian, the framework constructs the reversible sector, the associated spectral Hilbert space, and relational time evolution. Quantum dynamics is formulated through a Hamiltonian obtained as a spectral function of the Constraint Laplacian, leading to Schrödinger-type evolution within the emergent description. The paper further develops the symplectic structure of the reversible sector and relates quantum normalization to Planck’s constant. Observables are represented by self-adjoint operators, while spectral decomposition provides the basis for measurement probabilities and the Born-rule structure. Canonical position and momentum operators and their commutation relations are subsequently formulated within the same framework. The central objective is to present quantum mechanics as an emergent consequence of microscopic consistency dynamics rather than as an independent foundational postulate. The construction connects quantum states, dynamics, observables, measurement, and quantum normalization to a common spectral and constraint-based microscopic origin, providing the quantum-theoretical component of the broader Grand Consistency Theory research program.