Discovery Plane Theory: A Quantitative Framework for Scientific Discovery Based on Discovery Complexity and Question Compression

Scientific discovery is commonly studied through theories of information, computation, learning, creativity, and explanation. Existing frameworks primarily analyze information, descriptions, models, hypotheses, or solutions after a problem has already been formulated. However, comparatively little formal attention has been given to the discovery of questions themselves. This paper proposes Discovery Plane Theory, a unified framework for representing scientific discovery through two complementary quantities: Discovery Complexity and Question Compression. Discovery Complexity estimates the minimum effort required to generate a question from an observational domain and background knowledge, while Question Compression estimates the explanatory reorganization induced by that question. Together, these quantities define a two-dimensional Discovery Plane in which scientific questions are represented as points according to discovery effort and explanatory impact. The framework introduces Discovery Procedures, Question Compression, Discovery Complexity, Discovery Frontier, and the Discovery Scarcity Principle. A foundational optimization theorem is provided, and a preliminary historical dataset of fifteen major discoveries is used for exploratory validation. Results suggest that transformative discoveries tend to occupy high-compression and relatively high-complexity regions of the Discovery Plane. The dataset is not presented as a definitive measurement but as an initial operationalization of the proposed framework. The paper contributes a formal language for studying scientific discovery as a geometric process centered on the discovery of questions rather than only on the evaluation of answers.