The Structure of Possibility: Topological Constraints on Pre-Coherent Spaces

The Quantum Blueprint Formalism (QBF) presupposes a pre-coherent space M_s from which coherent structure is projected via π_Θ: M_s → M_Θ. Previous papers have characterized M_s functionally but not structurally. This paper derives the minimal topological, measuretheoretic, and algebraic structure that M_s must possess to support coherent projection. We establish four central results. First, M_s must be connected, Hausdorff, locally compact, and second-countable—the minimal structure for continuous projection and bounded compression. Second, the tension functional Φ: M_s → ℝ arises necessarily from the incompatibility structure of distinctions as the unique (up to monotonic transformation) measure of mutual incompatibility. Third, the probability measure ρ_s is uniquely determined (up to normalization) by the symmetries of the space—it is the Haar measure, and its projection yields the Born rule. Fourth, M_s is unique up to isomorphism. The deepest result: M_s is not a primitive posit but a self-generated structure—the closure of the distinction operation under self-application. M_s is not a pre-coherent space among alternatives but the unique structure of possibility.