Unti≈1000x Faster Lyapunov Spectra: Shannon-Truncated Tangent Propagation for the Kuramoto-Sivashinsky Equation on Low-Resource Hardware

Computing the full Lyapunov spectrum of spatiotemporal chaotic systems is prohibitively expensive: the standard Benettin algorithm with Gram-Schmidt reorthogonalization costs O(N^3) per time step when all tangent vectors are retained. We introduce a spectral truncation method that projects tangent vectors onto the Shannon-active sub-band (N/4 modes), reducing the effective cost to O(n_v * N log N) and achieving roughly three orders of magnitude speedup over naive full-spectrum computation. The technique exploits the spectral gap of the Kuramoto-Sivashinsky linear operator: modes beyond the cutoff wavenumber are damped 10^4 times faster than the largest Lyapunov exponent, carrying zero Shannon entropy about the attractor geometry. We compute the full spectrum (up to 341 exponents) for domain sizes L = 100, 150, and 200 entirely on low-resource ARM hardware (Snapdragon 8 Gen 2, NEON SIMD), with the largest case completing in 13 minutes -- a computation that required over 3 hours without truncation on the same device. The Kaplan-Yorke dimension scales as D_KY/L = 0.217 +/- 0.002, confirming extensive chaos in the thermodynamic limit. The method is hardware-agnostic and places full Lyapunov spectrum computation within reach of any system with an FFT implementation.