Effective Actions, Scale Flow, and Physical Equation Selection

SCQG paper 21 of 28 Paper 21 develops the equations that connect the microscopic dynamics of Semantic Commitment Quantum Gravity (SCQG) to physical fields at larger scales. An effective action collects the response of those fields to applied sources. The paper derives this action from finite history sums and tracks how its coefficients change as fine-scale degrees of freedom are removed. The construction keeps the microscopic boundary data, field normalization, operator mixing and mass thresholds consistent throughout the scale flow. Real-time equations use a closed-time-path construction, which evolves a prepared state forward and backward to calculate expectation values and causal response. Quantum channels describe the corresponding reduction of states and the loss of distinguishability between them. For chiral fermions, the paper constructs explicit finite overlap measures and checks their gauge symmetry, phase transport and locality. It gives a local measure with bounds uniform in temporal extent on the fixed spatial regulator, a construction using overlapping momentum regions for four-dimensional refinement, and conditions for joining local phase choices into a global continuum measure. These conditions include compatible phase conventions across refinements. The paper also derives the stiffness, relaxation rates, inertial stability and stochastic mixing of finite fragments. Endpoint amplitudes define positive preparation kernels, normalized states and action derivatives. The curvature calculation uses the same preparation family throughout, including direct curvature, changes in state fluctuations and the effect of eliminated fields. Conservation identities and explicit error bounds specify the domain of the resulting equations.