Discovery Plane Theory: A Formal and Reproducible Framework for Scientific Question Formation, Discovery Complexity, and Question Compression

Scientific discovery is typically formalised only after a problem or hypothesis has been specified, whereas the process by which a scientifically productive question emerges remains comparatively underformalised. This article introduces Discovery Plane Theory, a representation-relative framework in which each admissible scientific question is characterised by two coordinates: Discovery Complexity, the least admissible cost of generating the question from a Reality Space and background knowledge, and Question Compression, the nonnegative reduction in representational description length induced by the question. The theory provides an axiomatic foundation together with structural results on existence, bounds, invariance, dominance, frontier structure, metric geometry, temporal extension, and discovery scarcity. Eight algorithms operationalise coordinate construction, frontier extraction, benchmarking, reliability assessment, and approximate search within an auditable computational framework. To support empirical evaluation, we introduce DiscoveryBench v1.1.0, a reproducible candidate corpus comprising 1,500 field-validated OpenAlex records spanning Physics and Astronomy, Chemistry, Medicine, Computer Science, and Mathematics, together with a coding framework, validation scripts, and reproducibility resources. The corpus is explicitly intended as a screening frame rather than a set of pre-labelled discoveries. Discovery Plane Theory is therefore presented as a falsifiable mathematical framework linking formal definitions with independently coded empirical validation.