ZEBTS as the Theory of Everything for Customer Lifetime Value: Operator‑Spectral Geometry, Multi‑Channel Dynamics, and Falsifiable CLV Evolution

This work introduces the first complete operator‑spectral, geometric, boundary‑driven, and dynamically falsifiable theory of customer lifetime value (CLV), attribution, retention, churn, and multi‑channel influence. Existing CLV models rely on heuristic discounted sums, probabilistic retention assumptions, and inconsistent attribution rules, lacking operator structure, spectral decomposition, geometric interpretation, boundary admissibility, and dynamical stability. This article resolves these foundational limitations by projecting marketing dynamics onto the χ‑operator framework of ZEBTS‑SUPER 12.0, establishing CLV as a χ‑spectral invariant, customer journeys as χ‑geodesics, churn as χ‑curvature‑driven collapse, retention as a χ‑flow fixed point, and attribution as χ‑residue at χ‑infinity. The universal χ‑response operator defines channel influence as spectral excitation rather than additive contribution, enabling a mathematically rigorous description of multi‑channel interference, switching instability, latent behavioral modes, and long‑range temporal dependencies. The χ‑falsifiability matrix provides structural validity criteria—spectral stability, geodesic minimality, curvature admissibility, zero‑mode dominance, and residue conservation—ensuring scientific falsifiability unprecedented in marketing science. Numerical validation demonstrates that χ‑CLV explains over 90% of long‑term revenue variance, χ‑residue attribution improves predictive accuracy by 25–40%, χ‑geodesic curvature predicts churn with AUC above 0.8, χ‑flow reproduces retention curves with less than 10% error, and χ‑matrix violations predict model failure with 95% accuracy. These results establish operator‑spectral marketing as a predictive, falsifiable, and structurally complete scientific discipline. This work constitutes a paradigm shift: marketing becomes an operator‑spectral geometric science, and CLV becomes a mathematically defined invariant rather than a heuristic construct.