The Ontological Dominance Papers Theorem 1: The Law of Full Spectrum Dominance

This paper states the foundational theorem of The Ontological Dominance Papers: an entity achieves authoritative representation in AI-mediated information retrieval when its machine-readable authority signal construction rate exceeds the sum of parametric decay and competitive noise, sustained across architecture training cycles. We term this condition Full Spectrum Dominance (FSD), operationalized as unhedged citation probability at or above 0.75 across the full query distribution of a competitive category. The theorem identifies two structural advantages, temporal depth and vocabulary sovereignty, as resistant to competitive equalization, and specifies four conditions that must hold simultaneously for FSD to be achieved. This paper builds on and instantiates the governing inequality and measurement instruments presented in OD-S. The theorem is confirmed by independent mathematical analysis and by agent-based simulation across more than 5,000 parameter combinations; the designated primary falsification test is specified and scheduled, and empirical field confirmation is pending its execution.