On the Limits of Physical Verifiability of Theorems Concerning Prime Numbers

We live in a finite Universe. Yet mathematics speaks of infinity — and the Riemann Hypothesis, one of its greatest unsolved problems, asks a question about an infinite set of objects. In this work, I ask a deceptively simple question: what if the Universe simply doesn't have enough resources to ever fully verify the Riemann Hypothesis? I introduce the concept of the Limiting Informational Resource Γ and the Verifiability Height T(Γ), and I show that for any finite Universe, there exists a hard epistemic boundary beyond which the zeros of the Riemann zeta function can never be checked — not because they stop following the pattern, but because no certificate can fit within the available resources. The asymptotics are clean: T(Γ) = Θ(Γ / log Γ). The conclusion is striking: the Riemann Hypothesis is trans-empirical. It may be true. It may be false. But no finite observer can ever know for certain. This is not a mathematical proof — it is a philosophical framework, a set of axioms (A1–A5), and a thought experiment (W₁₀₀ — W₁₀⁶ — W_obs) that reframes the limits of mathematical knowledge as a consequence of physical finiteness. Originally born from a series of playful conversations between a human and an AI, this work is an invitation to rethink what it means to "know" a mathematical truth in a finite world. Follow my work and related discussions on Facebook: [Facebook]