URB #483 — The L*/+E Structural Proof: E-GIL Independence as Empirical Confirmation of the GILE Architecture

The measurement trilogy (URBs #480–482) established that conventional measurement systems capture only the E-dimension of the GILE framework, that physicalism is the philosophical root cause of this bias, and that the positive GIL data is real but abstract and filtered. This paper adds the algebraic closing argument: the empirical fact that E and GIL can vary completely independently of each other — in both directions, across all four quadrants of a High/Low × High/Low matrix — is not a puzzle requiring explanation. It is structural confirmation of the L*/+E architecture that the TI Sigma framework already formally predicts. In a tightly coupled system, E and GIL would correlate reliably over time, and the Inverse Metric Problem would be self-correcting. The observed complete independence proves they are not coupled. E is not derived from GIL. E is appended to GIL. That is what L*/+E means algebraically — and the empirical independence of E from GIL is the proof.