We introduce a formal framework for bounded evaluative architectures in which signal admission precedes task specification. The central object is a gating operator F1: S -> S' that constitutes a selection-conditioned subspace S' subset S prior to any encoding, learning, or reward optimisation. We prove three main results. First, valence-conditioned evaluation over S' is non-scalarizable (Theorem 2A-1): the multi-dimensional preference structure induced by selection-conditioned access violates the totality condition required for scalar representation, and selection-conditioning generates incommensurability — a strictly stronger failure — across distinct selection-conditioned submanifolds. Second, the evaluative state F2(t) satisfies a stochastic differential equation whose stationary distribution and stability properties depend on the selection hardness H_s(G) and noise variance sigma^2 (Theorems 2A-2, 2A-3). Third, the action-selection entropy exhibits a phase transition at the gating threshold: a discontinuity that cannot arise in scalar-reward systems with smooth policies, and that is architecture-invariant below the collapse threshold gamma* while architecture-dependent above it. We introduce Selection Hardness H_s(G) as a measurable quantity connecting these theoretical results to empirical predictions developed in the companion paper. This paper makes no empirical claims; all experimental validation is deferred to the companion empirical paper. Companion Papers: **Saka, H. (2026a).** Toward a Reframing of the Hard Problem of Consciousness: Subjective Reality, Feeling, andthe Origins of the Conceptual World. Version 7.19. PhilPapers. https://philpapers.org/rec/SAKTAR **Saka, H. (2026b).** Organizational Phenomenology: Artificial F1 and the Geometry of Coherent Agency. https://doi.org/10.5281/zenodo.20555024 **Saka, H. (2026d-Emperical).** Hard-Gating Collapse Dynamics: Selection Hardness as the Organizing Parameter for Robust Sparse Routing. https://doi.org/10.5281/zenodo.20523503 Keywords: selection-conditioned representation, non-scalarizability, selection hardness, phase transition, gating architecture, bounded evaluation, RLHF, dynamical systems