The Riemann Hypothesis as a Fixed-Point Phenomenon: Structural Parallels with Incompleteness and Undecidability

We identify a structural parallel between the prime-zero dependency cycle of the Riemann zeta function and the diagonal phenomena unified by Lawvere's fixed-point theorem (1969). Four conditions (D1-D4) are abstracted from the common structure of the liar paradox, Cantor's theorem, Gödel's incompleteness theorem, and Turing's undecidability theorem, and compared with the arithmetic of the integers. The Riemann Hypothesis is restated as a type-level characterization: all non-trivial spectral data lies in the fiber above the fixed point of the functional equation's involution. The Goldbach conjecture is positioned as a sibling coverage property of the same structural type. No theorems about zero locations are proved; the contribution is the structural correspondence and its conditional consequences.