What does this equation mean?

I define a compute-to-memory locality index, L , as the ratio of two bandwidth-per-joule figures: the realized random-access bandwidth a system can sustain across its full memory pool, divided by the power it costs to sustain that bandwidth, computed once for the optically unified case and once for the same total memory capacity attached the conventional way — as edge-limited HBM and DDR stacks wired electrically to a die of the same process generation. Here BW is realized, measured random-access bandwidth in bytes per second — not a marketing peak, not a sequential-streaming figure, since random access is what most large-model inference and any pooled-memory workload actually demands — and P is the power, in watts, that a system actually draws to sustain that bandwidth, attributable specifically to the memory-and-fabric subsystem rather than the whole machine. An index above 1 means the optical, unified case delivers more usable bandwidth per unit of energy than wiring the same total capacity to the die’s edge the ordinary way — a real, measurable locality gain, not just a capacity or reach gain. An index at or below 1, once the fabric’s own fixed integration overhead — the extra lasers, the photonic-PIC yield cost, the switch silicon itself — is amortized across a realistic deployment scale, is the condition under which “extension of the die” collapses into a more expensive way to get the same joules-per-bit a conventional design already gets, dressed in a bigger address-space number.