We can compress data far beyond Shannon's limits by only keeping the 'logical core' needed to re-derive the facts.

This new rate-distortion theory focuses on preserving 'deductive closure'—the ability to reach the same logical conclusions—rather than preserving individual symbols. It suggests we can throw away massive amounts of 'raw' data as long as we keep the 'seeds' required to re-calculate it. This is a paradigm shift for data storage and transmission: we don't need the data itself, just the logic. This could lead to a new generation of 'semantic' compression that is orders of magnitude more efficient than Zip or JPEG, particularly for large-scale knowledge bases and AI memory.