李雅普诺夫指数刻画动力系统对扰动的敏感性，而完整的李雅普诺夫谱则将其推广至切空间中每一正交方向。对于元胞自动机，该谱几乎总是通过数值方法近似计算，且近似过程十分微妙。本文证明：仿射规则（即其更新函数为输入子集的异或运算再加一常数）具有精确可解的李雅普诺夫谱。仿射规则的布尔雅可比矩阵与构型无关，因此其谱简化为某一固定常数矩阵的奇异值的对数，无需数值模拟，亦不涉及极限过程。其中两种情形具有闭式解：（1）在周期性格点上的仿射元胞自动机，其雅可比矩阵为多层循环矩阵，谱等于该规则梯度模板的离散傅里叶变换，适用于任意空间维度；（2）在任意图上定义的奇偶性规则，其雅可比矩阵即为图的邻接矩阵，故其李雅普诺夫谱为邻接谱绝对值的对数，最大李雅普诺夫指数为邻接矩阵谱半径的对数；此时单点扰动的长时间振幅按被扰动节点的特征向量中心性缩放。将周期性格点视为阿贝尔群的凯莱图，可统一上述两种情形。由于这些谱是精确的，它们亦可作为基准：不仅揭示了先前报道谱中出现的数值伪影，更将谱半径与动力学敏感性之间既往非正式的对应关系提升为严格恒等式。

The Lyapunov exponent quantifies the sensitivity of a dynamical system to perturbations, and the full Lyapunov spectrum extends this to every orthogonal direction in tangent space. For cellular automata the spectrum is almost always approximated numerically, and the approximation is delicate. We show that the affine rules, those whose update is a XOR of a subset of the inputs together with a constant, admit an exact Lyapunov spectrum. An affine rule has a configuration-independent Boolean Jacobian, so the spectrum reduces to the logarithms of the singular values of a single constant matrix, with no simulation and no limit involved. Two cases carry a closed form. For an affine cellular automaton on a periodic lattice the Jacobian is a multilevel circulant matrix, and the spectrum is the discrete Fourier transform of the rule's gradient stencil, valid in any spatial dimension. For the parity rule on an arbitrary graph the Jacobian is the adjacency matrix itself, so the Lyapunov spectrum is the logarithm of the absolute adjacency spectrum, and the maximal exponent is the logarithm of the spectral radius. The long-time amplitude of a single-site perturbation then scales with the eigenvector centrality of the seeded node. Reading the periodic lattice as the Cayley graph of an abelian group unifies the two cases. Because they are exact, the affine spectra also serve as benchmarks: they reveal numerical artefacts in previously reported spectra and turn the informal correspondence between spectral radius and dynamical sensitivity into an exact identity.