What if attention didn’t need matrix multiplication?

I built a cognitive architecture where all computation reduces to three bit operations: XOR, MAJ, POPCNT. No GEMM. No GPU. No floating-point weights. The core idea: transformer attention is a similarity computation. Float32 cosine computes it with 24,576 FLOPs. Binary Spatter Codes compute the same geometric measurement with 128 bit operations. Measured: 192x fewer ops, 32x less memory, ~480x faster. 26 modules in 1237 lines of C. One file.