Difference Is Distance (Space)

Fourth paper in the V=I series. Derives the geometry between multiple agents running the verification loop. When two agents operate independently over the same domain, their comparison caches diverge. The symmetric difference of these caches satisfies the axioms of a metric: identity of indiscernibles, symmetry, and the triangle inequality. Communication between agents costs at least one comparison per bit of cache difference. A speed limit follows: one bit of identification per comparison tick. Locality emerges from finite cache growth — agents with disjoint caches cannot influence each other's next comparison result. The metric is constructed entirely from the agents' recorded comparisons.