LC vacuum uncertainty ΔΦ·ΔQ = ℏ/2 (symplectic-capacity saturation by Gaussian vacuum)

LC ground-state Heisenberg uncertainty saturation. From framework F7, [Φ̂, Q̂] = iℏ implies ΔΦ · ΔQ ≥ ℏ/2 via Robertson-Schrödinger. The LC-oscillator ground state (Gaussian vacuum) saturates the bound: ΔΦ · ΔQ = ℏ/2 exactly. Zero-point…