HEXA-PHOTON: Photonic Matrix Multiply Engine with n=6 Interferometric Mesh

We present HEXA-PHOTON, a hybrid electro-photonic AI accelerator in which a silicon photonic matrix multiply engine performs linear algebra at the speed of light, with every design parameter derived from the arithmetic functions of the perfect number n = 6. The core compute unit is a \sigma \times \sigma = 12 \times 12 Mach-Zehnder interferometer (MZI) mesh implementing arbitrary 12 \times 12 unitary transforms via the Clements decomposition, requiring \sigma^2 = 144 MZIs in total. Wavelength-division multiplexing (WDM) with \sigma = 12 channels enables 12 independent matrix operations in parallel on a single photonic fabric. At \sigma - \tau = 8-bit phase precision (256 levels) and \sigma \cdot \tau = 48 GHz modulation rate, the engine achieves \sim5,000 TOPS equivalent throughput at \sim