Layered Neutrosophic Topo-Algebraic Framework for Analyzing the Adoption of National Standard Language and Script in Higher Education Institutions

The adoption of a National Standard Language and Script (NSLS) within higher education institutions is a complex, multi-layered process. It involves not only legal mandates but also cultural, infrastructural, academic, and institutional dynamics. Traditional binary logic and classical algebraic models fall short in evaluating such rich, uncertain, and often contradictory environments. This paper proposes a novel fixed, non-dynamic mathematical framework, Layered Neutrosophic Topo-Algebra (LNTA), to model and analyze institutional readiness for implementing NSLS. LNTA unifies neutrosophic algebra with layered topology by representing each institution as a multi-perspective entity, where each layer encodes trust (T), indeterminacy (I), and falsity (F) regarding a specific evaluation axis (e.g., legal, cultural, academic, infrastructural). The LNTA space is defined by a structured combination of a neutrosophic algebraic operator (∆) and a family of neutrosophic topologies (τ₁, ..., τₙ). The framework provides mechanisms to determine algebraic closure and topological openness in each layer, allowing for precise qualification of institutional subsets that are adequately prepared for NSLS adoption. Mathematical rigor is maintained throughout the model with multiple formal definitions, algebraic operations, and topological constructs. This work contributes a powerful algebraic-topological formalism to policy modeling, educational reform, and decision support in linguistically diverse settings.