Contextual Theory Systems: From Paper-Bound Knowledge to Callable Scientific Theory

Theoretical mathematics and theoretical physics already contain rigorous reasoning and trust boundaries, but those boundaries usually remain inside papers, specialist interpretation and local research environments. A result may be correct and still lack a stable identity, machine-readable scope, callable interface or reusable route into a new application. This paper proposes that the next major development of science will be a contextual theory system: a knowledge infrastructure that connects a theorem repository, a protocol for certificates and provenance, a contextual theory synthesis layer and a mathematical application layer. Computer science provides a development path for this transformation, from low-level semantic machinery to abstractions, libraries, interfaces and applications. The proposed system takes scientific theory as its object and uses computational machinery as its substrate: it combines formal theorems, regime-bound physical models, observations and open hypotheses while preserving their different evidence contracts. A future autonomous spacecraft is a motivating situation: it may need to select and combine theories under an unfamiliar physical regime, generate a bounded local model, and act while recording which parts are proved, model-dependent or provisional. The central prediction is that increasing proof supply, scientific complexity and autonomous application pressure will force some such callable theory layer into existence. The prediction is testable through independent-use cost, semantic transport, model-selection and maintenance measurements.