nx_fnet_mix_gate.nx

nx_fnet_mix_gate.nx -- GATE for FNET-001 sub-quadratic Fourier token-mixer. Proves, by RUNNING (never asserting): CORRECTNESS C1 the generalized radix-2 FFT equals the naive O(n^2) DFT (same Q14 twiddles) at n=8 and n=16 -- the butterfly decomposition is algebraically a real Fourier transform, not loop-counting. C2 the synthesized n=32 twiddle table matches the SHIPPED, gated nx_fft hardcoded W_32 table within 1 Q14 unit -- so it is the SAME transform as the proven kernel, just generalized past N=32. MEASURED SUB-QUADRATIC EXCEED (the thesis: math kills the VRAM/compute exponential) For hidden dim d=16 and sequence lengths n in {64,256,1024,4096}, both kernels are RUN on real deterministic data and their executed integer-MULTIPLY counts are measured: attention = scores(Q@K^T, n*n*d) + softmax-normalize(n*n) + apply(@V, n*n*d) = 2*n^2*d + n^2 (O(n^2)) fnet-mix = 2*n*d*(log2 d + log2 n) (O(n log n)) (softmax's transcendental exp is excluded for BOTH as a non-MAC, the standard FLOP convention; the two O(n^2*d) matmuls are the attention cost present in every attention variant.) Each measured count is asserted EQUAL to its structural closed form (the counter is faithful), and the gate proves: fnet_mul < attn_mul at every n, AND the attn/fnet ratio STRICTLY GROWS with n -- the quadratic-vs-linearithmic crossover, compounding as context lengthens. A real output checksum from each kernel is printed so the work cannot be dead-code-eliminated. Evidence -> knowledge/status/fnet_mix.log (FNETGATE authored=organ ... verdict=GREEN). license_tier: ORIGINAL