The M.A.T.H. Framework: A First-Principles Approach to Quant Marketing in High-Uncertainty Environments

The digital advertising ecosystem generates data volumes exceeding human cognitive processing capacity by orders of magnitude, while simultaneously degrading data quality through invalid traffic, attribution fragmentation, algorithmic opacity, and privacy-driven observational collapse. This paper formalizes the resulting structural mismatch, the Linear-Exponential Gap, between exponential growth in market complexity and approximately logarithmic growth in human analytical bandwidth. We introduce the M.A.T.H. Framework (Measure, Analyze, Tweak, Harvest), a recursive optimization protocol whose four stages address the principal failure modes of modern advertising operations: data corruption (Measure), confounded inference (Analyze), insufficient experimental velocity (Tweak), and suboptimal scaling (Harvest). We develop the information-theoretic foundations of each stage, including formalization of the data processing inequality as a bound on optimization performance, causal inference methods for deconfounding observational data, the Cycle Velocity construct for quantifying experimental throughput, and marginal economic analysis for identifying optimal scaling boundaries. System-level analysis demonstrates convergence properties governed by the Effective Learning Rate and degradation dynamics governed by creative fatigue, competitive displacement, and algorithmic drift. We establish conditions under which the framework achieves antifragility: converting environmental volatility into informational advantage. The framework operates on aggregate data rather than individual-level tracking, making it structurally compatible with privacy regulation and invariant to ongoing reductions in user-level observability.