Three foundational problems in the philosophy of science have resisted solution for decades or centuries: the demarcation problem (what distinguishes science from pseudoscience), the underdetermination problem (how to choose between empirically equivalent theories), and the halting-problem analogue for theory confirmation (whether any general procedure can determine if a theory will be confirmed or refuted). This paper demonstrates that the Triveritas, the triadic epistemological criterion requiring the simultaneous satisfaction of logical validity (L), mathematical coherence (M), and empirical anchoring (E), solves all three problems simultaneously using a single architectural mechanism: structurally warranted termination. Scientific theories are modeled as recursive structures whose confirmation chains terminate at base cases dictated by the mathematical structure of the theory itself. The demarcation problem is solved because pseudoscience fails to reach structurally warranted base cases. The underdetermination problem dissolves because competing theories evaluated on three independent dimensions are almost never equivalent on all three. The halting-problem analogue is resolved by the distinction between general undecidability and specific provable termination. No new machinery is introduced. The solutions follow from the existing Triveritas framework applied to the epistemology of science.
