Clarification and Generalization of the Restricted z-Framework with Boundary Alignment and Indexed Hadamard Factorization

This paper clarifies and extends the restricted-variable framework introduced in Drake (2026). Restriction does not alter the underlying analytic object, provided the restricted and unrestricted presentations agree on a nonempty open overlap domain; it changes only the regime of admissible access. In the model case of the completed Riemann zeta function, the paper shows that functional symmetry acts on the argument of the function but does not by itself induce an admissible zero-indexing rule in the restricted Hadamard product. As a result, reflected zeros remain analytically present through symmetry, yet do not appear as separately admissible geometric indices unless they lie on the symmetry boundary. This yields the Hadamard representation dilemma that consistency between canonical Hadamard factorization and the restricted admissible indexing mechanism forces the nontrivial zeros onto the critical line. The same mechanism is then extended to entire functions of order one satisfying a reflection symmetry under an optimal half-plane restriction. The paper also shows that symmetric linear combinations do not constitute counterexamples, since their zeros arise through cancellation rather than through the restricted zero-indexing mechanism.