The Ontological Dominance Papers Theorem 3: The Portfolio Extension

This paper states Theorem 3 of The Ontological Dominance Papers, the Portfolio Extension, governing organizations that compete across multiple product or service categories. The theorem establishes that total AI representation across a multi-category portfolio is not the unweighted average of per-category authority but the prominence-weighted average, where prominence is the fraction of total buyer queries falling into each category. The theorem specifies a quarterly monitoring and reallocation protocol and characterizes cross-category spillover as a benefit when categories share vocabulary and buyer type, and a liability when they do not. Building on the mathematical foundation in OD-S and extending OD-1, Theorem 3 was classified VERDICT B upon adversarial review: a formally correct extension of OD-1's scope conditions, not an independent theorem, confirmed by three independent mathematical derivations and contingent on OD-1's empirical field confirmation, which is pending execution.