Reasoning
The fitted relation is serum cholesterol proportional to the square root of dietary cholesterol dose. The derivative of sqrt(x) is 1/(2*sqrt(x)), a strictly decreasing function of x. Hence the marginal serum-cholesterol rise per additional mg of dietary cholesterol is largest near zero intake and shrinks monotonically as habitual intake grows: adding one egg (~185 mg) to a low-cholesterol diet moves serum cholesterol more than adding the same egg on top of an already-high-cholesterol diet. A linear model, by contrast, assigns a constant marginal effect and therefore overstates the incremental harm of extra eggs for people already eating substantial cholesterol. This is a purely mathematical consequence of the concavity of the fitted curve, independent of the mechanism.
Step 6 verdict
approved / checked. Purely mathematical and verified directly: for S(x) = ksqrt(x), S’(x) = k/(2sqrt(x)), which is strictly decreasing on x>0, and S is concave (S” = -k/(4*x^(3/2)) < 0). Hence the finite increment S(x+185) - S(x) is strictly decreasing in x, which is exactly the claim about an added egg at higher baseline intake, and a linear fit calibrated at low intake necessarily overstates that increment at high intake. Scope caveat that does not affect validity: the conclusion holds only inside the fitted 50-1450 mg/d range, and it is a statement about the fitted curve, not about whether the square-root form is the correct functional description — the latter is a premise, priced downstream.