Generative Reuse in Theoretical Derivation: Intra-Derivational Choices, Local Non-Rigour, and the Production of New Results

Mathematical and scientific derivations are often presented as sequences of inferential steps proceeding from established premises toward a conclusion. This representation obscures a class of activities that occur throughout the derivation process: researchers introduce definitions, assumptions, constraints, auxiliary structures, approximations, and representational choices that are not uniquely determined by the preceding steps. Such choices may be made because they activate existing mathematical or scientific derivation mechanisms, permit their application under transformed conditions, or enable several previously available mechanisms to be recombined into a new inferential route. This paper develops a conceptual account of these activities under the name generative reuse in theoretical derivation. The central thesis is that theoretically productive derivation involves not only the application of established inference rules but also the repeated selection and modification of conditions under which existing inferential resources can operate. These selections may occur at the beginning of a theory, at intermediate stages, or immediately before a subsidiary derivation. Their significance therefore cannot be reduced to the initial assumptions of a theory or to the subsequent evaluation of a completed model. They can be constitutive of the ongoing production of theoretical results. The paper distinguishes generative choices from ordinary deductive steps, classifies their principal forms, and proposes a process model connecting derivational states, local choices, reusable inference mechanisms, and result evaluation. It also develops a qualified account of local inferential non-rigour: a gap arising when an indispensable assumption, constraint, or applicability condition is insufficiently established, rather than merely non-unique or non-deducible. Examples from mathematical practice, scientific modelling, and quantum field theory illustrate both the explanatory potential and the limitations of the proposal. The resulting account treats theoretical progress as a process of goal-constrained, resource-sensitive, and context-dependent inferential construction. It explains how derivational creativity can arise through the transformation and recombination of established methods without implying that successful reuse guarantees truth. The paper concludes by identifying criteria for distinguishing justified generative choices from choices that merely facilitate the derivation of a desired conclusion.