Three Spectral Theorems in Information-Dynamic Theory: Bilateral M Bound, Propagation Speed, and Critical Exponent Condition

This preprint establishes three canon-derived spectral theorems in Information-Dynamic Theory (IDT): a tight bilateral bound on structural inertia, a propagation speed bound, and a precise condition for non-classical critical slowing down. Theorem 1 proves the inequality 1 ≤ M (ω) ≤ κ (G⁻¹H), where κ is the spectral condition number of the generalised eigenvalue problem. Theorem 2 derives a bilateral bound on the information propagation speed. Theorem 3 establishes the exact spectral condition under which the physical relaxation time scales as τₚhys ~ ε^ (−2β), distinguishing IDT from standard critical slowing down. All results require no new axioms and are directly verifiable on any GEP spectrum.