The Measurement Problem as a Category Error: A Mathematical Proof of Wavefunction Unobservability

We prove rigorously that the quantum mechanical wavefunction ψ is mathematically unobservable using information theory, set theory, and Hilbert space analysis. The proof establishes quantitative bounds: reconstruction error scales as ∥ψ − ψ̃_N∥² ≥ C/N² due to the uncertainty principle, making exact recovery impossible with finite measurements. This demonstrates that quantum mechanics is a statistical theory, firmly rooted in Unitary Mathematics — a framework previously instrumental in eliminating dark matter in galactic dynamics. The measurement problem dissolves when wavefunction realism (a category error) is replaced with statistical interpretation. We present three quantified falsifiable predictions, preemptively respond to objections (weak measurements, Bell inequalities, quantum computing), prove that wavefunction tomography cannot violate our bounds, and provide a constructive framework for doing quantum mechanics without wavefunctions. The parallel to dark matter elimination is exact: both are "Ghost Space" artifacts arising from mistaking mathematical tools for physical entities.