Bounded and Unbounded Infinity: A Structural Interpretation of Millennium Problems

Major unsolved problems in mathematics share a common structure: they require reconciling discrete generation (unbounded perspective) with continuous description (bounded perspective) of infinity. The Riemann Hypothesis asks whether spectral analysis (bounded/continuous) can predict number-theoretic structure (unbounded/discrete). P versus NP asks whether complexity characterization (bounded) equals algorithmic generation (unbounded). We argue these problems approach structural floors where both perspectives become simultaneously necessary yet fundamentally incompatible within a single framework. This incompatibility follows from Gödel's incompleteness: systems cannot fully characterize themselves from within. We examine the Millennium Prize Problems through this lens, showing how each sits at the discrete-continuous boundary. We conclude that certain problems are structurally complete precisely because they are formally unsolvable, reaching what we call the paradox of the structural floor. The paper forms part of a broader research corpus examining structural duality, invariant identity, and the limits imposed by observation and formal systems.