Saturn Heavy-Element Budget and Dilute-Core Extent from Cassini Gravity and Ring Seismology Constraints

This paper computes a quantitative budget for the deep interior of Saturn from published spacecraft values, using a deliberately transparent calculation whose every step can be checked from the deposited script. The headline results are: heavy_element_earth_masses = 12 to 18; heavy_mass_fraction_percent = 12.6 to 18.9; enrichment_over_solar = 8.41 to 12.6; dilute_core_volume_fraction_percent = 12.5 to 21.6; planet_mass_earth_masses = 95.17. Saturn's heavy-element mass fraction is markedly higher than Jupiter's even though the absolute inventory in Earth masses is smaller, a direct consequence of Saturn's lower total mass: the same solids budget enriches a smaller gas reservoir more strongly. The volume share of the graded central region is between an eighth and a fifth of the planet, far larger than the few percent a compact core would occupy, which is why the stratification it implies can plausibly suppress deep convection and help maintain the region in which helium separation occurs. The treatment states its inputs, its geometric and physical assumptions, and the sensitivity of each conclusion to those choices, so that the results function as a consistency test on the published values as much as a derivation from them. Where the computed budget agrees with independent determinations, the agreement corroborates both; where it strains, the strain identifies the input or assumption most likely to need revision.