Observational Constraints on Geometric Operator Algebra Cosmology from N=1590 Pantheon+ Supernovae and Theoretical Primer

This study presents the formal mathematical framework and observational validation of the Topological Spectacle Operator Model, a geometric theory that resolves cosmological acceleration through an intrinsic topological operator without invoking an ad-hoc cosmological constant (Λ) or dark energy fluid. By establishing a rigorous mapping between the geometric topological index and the effective equation of state, the framework overcomes the redshift dilution and observational tension inherent in earlier heuristic models. These results demonstrate that the spectacle operator acts as a rigid, fundamental geometric invariant in physical spacetime. This work presents an observational and theoretical study of Geometric Operator Algebra Cosmology. Utilizing the full Pantheon+ Type Ia Supernova dataset ($N = 1590$), we constrain cosmological parameters and evaluate 1σ and 2σ confidence ellipses against observational data. In addition to observational fitting, this manuscript includes an integrated, self-contained theoretical Primer (Theoretical Section) detailing the mathematical foundation from background operator algebra formulations to explicit geometric operator definitions and theoretical derivations. Full observational constraint using $N = 1590$ Pantheon+ Type Ia Supernovae dataset. Precise mapping of 1σ and 2σ joint parameter confidence contours. Self-contained theoretical Primer on Geometric Operator Algebra without reliance on traditional phenomenological approximations. Complete presentation of numerical results, analytical operators, and structural figures.