The Dynamic Meta-Measurement Homomorphism Law (DMHL)

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This paper establishes The Dynamic Meta-Measurement Homomorphism Law (\Omega\text{DMHL}), establishing a mathematical and cybernetic framework for zero-disparity system evaluation across arbitrary N-node network topologies. We prove that classical static measurement metrics inevitably induce scale-induced distortion when evaluating high-frequency, multi-depth, or non-linear processes. By constructing a self-calibrating meta-measurement tensor (\mathcal{M}_{meta}(t)) homomorphic to the system's operational state space (S(t)), we eliminate evaluation residuals (E_{disparity}(t)\rightarrow0). The framework is scale-invariant (N\ge1), medium-neutral, metric-agnostic, and security-independent. We demonstrate \Omega\text{DMHL} across 10 extensive real-time case applications including an epistemic cognitive frequency meta-scale alignment archetype detail resolved scientific challenges, define Popperian falsifiability conditions, and provide an executable computational Python model.