μ·HVL = ln 2; TVL/HVL = log(10)/log(2) ≈ 3.32

Sympy-exact symbolic witness of the HVL / TVL relations. Step 1 — HVL from Beer-Lambert: I(HVL) = I₀ / 2 gives exp(−μ · HVL) = 1/2, thus μ · HVL = ln 2 (sympy literal 'log(2)'). Step 2 — TVL: I(TVL) = I₀/10 gives μ · TVL = ln 10…