On the basis of a recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, L, controlled by the frictional coefficient, α(T)≪1, responsible for the cutoff. The curve ln L(ln⁡α) is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wave number regions. Excellent agreement with a recent experiment by Walmsley et al. [Phys. Rev. Lett. 99, 265302 (2007)]—in which L(T) has been measured down to T∼0.08  K—implies that the scenario of low-temperature superfluid turbulence is now experimentally validated and allows to quantify the Kelvin-wave cascade spectru