Curvature as a Measure of Interpretive Load

This registration documents Curvature as a Measure of Interpretive Load, a structural analysis of how accumulated coherence compresses semantic space and increases the effort required to introduce, sustain, or revise distinctions within meaning-bearing systems. The work introduces semantic curvature as a relational measure for describing interpretive load, rather than as a numerical metric, operational indicator, or optimization target. The analysis reframes stability and coherence as conditions that carry structural cost. As interpretations, categories, and representations accumulate, semantic space deforms, producing curvature that reshapes interpretive movement. In highly curved environments, some interpretations become easy and natural to sustain, while others encounter steep resistance regardless of their logical validity or relevance. Interpretive difficulty is thus treated as a function of structural compression rather than complexity, disagreement, or bias. This project distinguishes curvature from bias, distortion, or ideological skew. Curvature is defined as a content-independent structural condition that favors continuity and stability over deviation and revision. A system may exhibit extreme curvature even under conditions of technical accuracy, procedural correctness, or normative neutrality. Curvature explains how systems can appear coherent, aligned, and mature while becoming increasingly resistant to alternative interpretation. The registration situates curvature as a foundational mechanism within the broader structural ecology articulated in earlier registrations. Rising curvature is shown to produce premature coherence by compressing semantic space before exploration is complete, and to contribute to irreversibility by raising the cost of reopening collapsed distinctions beyond reconstructive capacity. Semantic propagation follows curvature gradients, while boundary failure and proxy substitution further intensify compression. Particular attention is given to AI-mediated environments, where representational persistence, probabilistic smoothing, and reinforcement mechanisms accelerate curvature accumulation. In such systems, coherence is not merely reflected but actively stabilized, shifting interpretive load from human judgment to structural constraint. Meaning becomes easier to reproduce and increasingly costly to revise. The analysis is intentionally non-prescriptive. No curvature metrics, computational measures, governance thresholds, or optimization strategies are proposed. Curvature is presented as a condition to be recognized rather than a parameter to be managed. The purpose of this registration is conceptual and structural: to clarify how interpretive load emerges from accumulation and why stability is often misinterpreted as neutrality or resolution. This description reflects an open-ended theoretical articulation rather than a finalized framework. The concepts documented here establish semantic curvature as a non-quantitative structural measure that may inform future analytical, empirical, or applied work within the Meta-Writing Ecology. Part of Meta-Writing Ecology — metawritingecology.org