Abstract Wolfram's Principle of Computational Irreducibility asserts that for most non-trivial discrete systems there exists no analytical shortcut: to determine the state at time T, one must simulate all T steps. For finite-dimensional unitary graph systems, the evolution admits an exact spectral representation for a specific class of systems: finite quantum graphs with unitary evolution. Knowledge of the spectral slice - the quantum state |Ψ(t₀)⟩ and the spectrum of the evolution operator Û - fully and exactly determines the state at any moment T without stepping through intermediate times. The theorem is a principled, not a practical result: algorithmic complexity O( ) remains exponential. Practical significance is achieved in the coarse-graining limit at scale ℓ >> a, where the problem reduces to polynomial complexity. Three conditions - finiteness, unitarity, linearity - constitute the exact domain of applicability.