Riemann Hypothesis

The simplicity and evenness of the Weil minimum state, as well as its agreement with the prolate approximation, have not yet been proven. Therefore, I further abstracted the problem and examined whether the completed zeta structure has a "mirror" that reflects left and right, and whether there is a mechanism that does not allow anything outside the critical line. However, it became clear that deriving this mechanism unconditionally leads back to the same barrier as the known Riemann Hypothesis. Furthermore, it became evident that even if another complete picture with the correct properties could be created, it does not necessarily mean it is the same as the actual zeta.

Since the last time, instead of simply following the equations, I have abstracted the structure multiple times by substituting it with elements like the resonance in the acoustic room, the collision between bullets, and the retrieval of narrative foreshadowing. Within this process, I reexamined the idea that "primes, Gamma, and theta are not separate forces, but instead emerge from the same singular zeta structure as a result of trying to satisfy all consistencies." I also confirmed, through known characterization theorems, that when certain conditions are simultaneously met, the zeta function is almost uniquely determined. Furthermore, by reviewing existing research, I realized that the finite test functions and the operator theory with fixed ranges I was trying to create could rely on established theorems. Consequently, I narrowed my remaining research focus to the "simplicity and parity of finite ground states" and the "comparison between actual ground states and the prolate approximation."