Theory Generation as Constraint-Governed Covering, Refinement, and Local-Global Compatibility

This paper proposes a framework for understanding theoretical plurality across disciplines by modeling a theory not primarily as a set of propositions, but as a covering structure on a high-dimensional, irregular explanatory domain. The central claim is that a theory is generated through a choice of coarse explanatory cover, and subsequently developed by refinement under constraints. The key scientific-philosophical question is not only how a theory is refined once it exists, but which theories can exist at all: that is, the structure of the possibility space of theories. We show that domains with weak refinement constraints admit many distinct generative starting covers, thereby allowing persistent theoretical pluralism, while domains with strong structural constraints admit only a narrow family of viable starting covers and thus exhibit convergence toward a small number of formalized theories.

To make this idea mathematically precise without overcommitting to assumptions that may fail, we develop a conservative formal framework based on covering systems, refinement preorders, admissibility constraints, and a presheaf-like organization of local explanations. We define a theory generation space as the collection of coarse covers that admit at least one infinite or sufficiently long refinement chain satisfying the relevant constraints. We then interpret theory maturity as a local-to-global compatibility property: a mature theory is one whose local explanatory pieces can be coherently glued into a globally coherent account. Under additional hypotheses, one may further study obstruction phenomena by cohomological methods, but we explicitly isolate those as conditional extensions rather than necessary components of the theory.

The framework yields a unified account of theoretical multiplicity, methodological conservatism, the relation between falsifiability and structural constraint, and the difference between pluralistic fields such as many areas of the humanities and social sciences and highly constrained formal domains such as mathematics and parts of theoretical physics. The paper concludes by outlining directions for further formal development, including the geometry of theory space, branching and collapse of refinement trajectories, and the study of compatibility obstructions.

Keywords: theory generation, covering refinement, scientific pluralism, philosophy of science, presheaf, local-global compatibility, refinement space, theory space