With the discovery of their level error by GIT, the Riemann and Collatz conjectures are confirmed in their own structure

ABSTRACT This study reinterprets two of the most prominent unsolved problems in mathematics—the Collatz conjecture and the Riemann hypothesis—through the lens of Holistic Information Theory (HIT). Both problems, long regarded as paradoxical, are shown to be based on a fundamental level error: the confusion between finite processes that unfold in space-time and the infinite potential of dimension 0. By introducing a clear separation of these levels, HIT demonstrates that neither Collatz nor Riemann are unsolvable puzzles. Instead, they appear as consistent manifestations of universal laws of information. Collatz sequences, previously suspected to allow infinite orbits, are explained as necessarily finite, converging to the cycle 4→2→1. Likewise, prime numbers are redefined as elementary units of information, with the critical line Re(s) = 1/2 representing an axis of equilibrium between information potential (dimension 0) and realisation (space-time). The study further integrates perspectives from philosophy, physics, and consciousness research, highlighting that information, mathematics, geometry, and self-awareness must be understood as interconnected natural laws. Their synergy forms the foundation of a broader law of information governing not only mathematical processes but also biological, cognitive, and cosmological evolution. Thus, the Collatz and Riemann conjectures are not unresolved anomalies but confirmations of HIT’s core principle: the structure of reality emerges from the ordered interaction between finite and infinite levels of information.