The Unified Operator: Algebraic Foundation for Zero-Parameter Physics

We present the complete operator formalism unifying D-space dimensional analysis, Riemann Hypothesis constraints, Birch-Swinnerton-Dyer elliptic structure, and Weyl chiral symmetry into a single mathematical framework. The unified operator acts on an 840-dimensional Hilbert space determined by the Cassini invariant |I| = 29. Physical particles correspond to simultaneous eigenstates satisfying four geometric constraints: (i) D-space dimension eigenvalue, (ii) Riemann critical line Re (s) = 1/2, (iii) BSD rational point structure, and (iv) Weyl fold symmetry D (x) + D (1/x) = 0. We derive the zeroparameter observable prediction formula Ψ (r) as diagonal matrix elements of B, proving all framework constants emerge from operator eigenvalues. The formalism provides geometric interpretation of the 14 verified physical observables and establishes testable predictions through operator rank constraints.