Constructing Theorem-Level Questions: A Declaration Discipline for Bounded Inquiry

This paper proposes a methodology for constructing theorem-level questions through explicit declaration rather than implicit assumption. It identifies six components required for a mathematically well-typed question—object, admissible transformations, observable, equivalence relation, verdict class, and stopping condition—and develops a declaration discipline for moving from informal prompts to decidable mathematical statements. The paper separates asking, typing, computing, and interpreting into distinct stages of inquiry and introduces three reusable artifacts: a six-component question type, a proof-obligation checklist, and a layered status discipline distinguishing mathematics from derived consequence, interpretation, speculation, and open problems. A neutral worked example from program equivalence demonstrates the methodology independently of the author’s other research. The paper argues only that theorem-level questions require sufficient declaration of their governing regime; it does not claim that all meaningful inquiry should be formalized. The result is presented as a methodological framework for constructing and auditing formal questions across mathematics, computer science, and related technical disciplines.