State-Space Lift of the Smith Chart

This preprint introduces a state-space lift of the Smith Chart, Σ(ω,t) = (ReΓ, ImΓ, χ), where χ(ω,t) = |∂Γ/∂logω| is the local dispersive sensitivity — the 1-jet of the reflection curve in the log-frequency variable. The lift is derived from Maxwell's equations and validated to 0.11% error. Six formal properties are established (Propositions A1–A6): exact collapse to the classical 2D Smith Chart (A1), non-redundancy — two loads with |Γ₁−Γ₂| = 5.6×10⁻¹⁷ at 60 GHz but |χ₁−χ₂| = 0.0035 (2.0%) — (A2), H¹-monotonicity confirmed over 147 tests with zero violations (A3), Fisher information gain ≥ 1.0 everywhere with up to 1.62× at 300 GHz (A4), estimation error bound with optimal step h* (A5), and information gain with Jacobian conditioning trade-off (A6). Cole–Cole simulations of four physiological states of skin tissue across 30–300 GHz yield +19.6% discriminability improvement 95% CI: 17.4%, 22.1% over the classical 2D Smith Chart. Extended computational validation using IT'IS Foundation v4.1 parameters (6 tissue types) yields +123% improvement. Monte Carlo validation over n=500 virtual subjects yields Cohen's d = 1.49–1.54 (p < 0.001). Peak dispersive sensitivity occurs at ~45 GHz (FR4 band), coinciding with the maximum Fisher information gain — connecting spectral geometry, information theory, and engineering frequency selection in a single operating point. The framework is most immediately useful for frequency selection, spectral discrimination, and regularized observation. Submitted to IEEE Access for peer review.