Non-Euclidean Normative Space: When Legal Hierarchies Curve Extended Phenotype Theory, Lateral Silencing, and the Geometry of Legal Systems Beyond Kelsen

Legal positivism, from Kelsen through Hart and their contemporary successors, operates on an implicit geometric assumption: the normative space in which law functions is flat. The Kelsenian pyramid presupposes five properties of Euclidean normative space: each norm has a single declared function; validity flows in one direction, from superior to inferior; the causal effects of a norm are proportional to its hierarchical rank; formal invalidity tracks functional failure; and norms in distinct regulatory domains operate on parallel tracks that never intersect. This paper argues that these properties hold only in a limiting case, specifically, in systems where norms are structurally enforceable, where enforcement is systematic rather than discretionary, and where the secondary effects of norms are negligible relative to their primary regulatory functions. When those conditions are not satisfied, the normative space curves. Also, this paper develops a framework for analyzing the geometry of curved normative spaces, drawing on three theoretical resources that have not previously been combined in this way: the Extended Phenotype Theory of Law (EPT; Lerer, 2026a), which identifies legal norms as cultural replicators whose effects extend well beyond their declared regulatory domain; the Lateral Silencing Exaptation (LSE; Lerer, 2026b), which formalizes the mechanism by which structurally unenforceable norms suppress political contestation across domains; and the mathematical tradition of non-Euclidean geometry, understood not as a technical apparatus but as a conceptual framework for thinking about spaces in which the standard axioms fail. The paper proceeds in five stages. First, it reconstructs the implicit Euclidean geometry of the dominant traditions in legal theory, showing that Kelsen, Hart, Fuller, Raz, and their contemporary successors all presuppose flat normative space, even when they disagree on every substantive question. Second, it identifies the conditions under which normative space curves, developing a taxonomy of curvature types corresponding to the three failure modes identified in LSE theory. Third, it proposes three specific non-Euclidean geometries as candidates for modeling curved normative spaces: Riemannian geometry for systems of high lateral silencing density; hyperbolic geometry for systems of high modularity and domain separation; and a quantum superposition model for norms whose functional state is indeterminate until the enforcement act collapses it. Fourth, it connects this geometric framework to the existing diagnostic instruments of the EPT research program, showing how the Constitutional Lock-in Index, the Institutional Hysteresis Rate, and the Lateral Silencing Index can be understood as measures of curvature in normative space. Fifth, it considers the implications of non-Euclidean normative space for legal theory, legal design, and the philosophy of law. The paper closes with five falsifiable predictions.