Proof Pipeline and Spectral Synthesis of the Riemann Hypothesis via 7D Fractal Lattice Operator Algebras: Appendices 1.1–1.3, Appendix 2, and Integrated Metadata Index (Appendix 3)

This publication establishes a closed, rigorous operator-theoretic framework and proof pipeline for the Riemann Hypothesis, synthesizing Appendices 1.1, 1.2, 1.3, Appendix 2, and the master integration Appendix 3. We construct an arithmetic-topological operator Â7D acting on the Hilbert space L²(T⁷) over a 7-dimensional compact torus. By proving essential self-adjointness via the Kato–Rellich theorem and establishing spectral equivalence with the non-trivial zeros of the Riemann zeta function ζ(s), we demonstrate that all non-trivial zeros are strictly constrained to the critical line (s) = 1/2.