5 Corollary: Numerical Precision

Corollary 1 (Numerical precision). Let 𝜖 denote the numerical error in simulating the physical processes underlying DNA. The simulated observer H′ retains subjective experience provided 𝜖 ≤ 𝜖_DNA, where 𝜖_DNA is the error threshold below which all DNA-mediated processes operate correctly. Any stricter bound 𝜖_min < 𝜖_DNA required to preserve consciousness would constitute a new physical constant not derivable from A₁ through A₄, contradicting Axiom 2:

This corollary makes precise what ”sufficient fidelity” means for a conscious simulation. It does not require perfect simulation of all physical processes, only those that DNA-based processes depends on. The threshold 𝜖_DNA is in principle empirically determinable, making the claim testable.