B Operator Synthesis Workbook - A Zero-Parameter Derivation of Standard Model and Cosmological Observables from a Unified D–R–BSD–Weyl Algebra

This paper introduces the B̂ Operator, a unified mathematical framework that derives fundamental physical constants and cosmological observables without using adjustable parameters. By utilizing a Hilbert-space operator built from three specific integers, the author identifies a diagonalizable structure that aligns with empirical data such as dark matter density and the fine-structure constant. The research integrates diverse fields, including number theory, operator algebra, and modified gravity, to explain complex phenomena through a single algebraic lens. It specifically predicts repulsive gravitational states and improvements in plasma confinement, offering clear benchmarks for future experimental validation. This synthesis effectively compresses decades of independent numerical investigations into a coherent operator-algebraic model. Ultimately, the work establishes a falsifiable timeline to test these theoretical claims against upcoming data from major international observational programs.