The fitted model is ΔChol = 1.5·(Z2 − Z1) where Z = √C and C is dietary cholesterol in mg/1000 kcal (corroborated verbatim form; the same term enters the combined Keys equation ΔChol = 1.2·(2ΔS − ΔP) + 1.5·ΔZ). Treating serum cholesterol as f(C) = 1.5·√C, the marginal effect is df/dC = 1.5/(2·√C) = 0.75/√C, which strictly decreases as C rises — this is the mathematical content of “diminishing returns / concavity.” Worked illustration: raising C from 100 to 200 mg/1000 kcal gives Δ = 1.5·(√200 − √100) = 1.5·(14.14 − 10.0) = 6.2 units, whereas raising C from 400 to 500 gives Δ = 1.5·(√500 − √400) = 1.5·(22.36 − 20.0) = 3.5 units — a smaller rise for the same 100-unit increment at higher baseline. The inference bears on the feeding observation (O-28): the same data that show cholesterol rising with intake, read through this concave fit, imply that at habitual dietary-cholesterol intakes an extra egg’s worth of cholesterol moves serum cholesterol only modestly. The relation is a fitted mathematical form; its validity as a description is what steps 6/8 assess, but the concavity → small-marginal-effect implication is arithmetic given the form.
Validity verdict — approved (checked)
Traced the load-bearing step myself (elementary, author-blind). Take the form as premised: f(C) = 1.5·√C. Then df/dC = 1.5 · (1/2) · C^(−1/2) = 0.75/√C, which is strictly decreasing in C — the derivative falls monotonically, i.e. the function is strictly concave (f” = −0.375·C^(−3/2) < 0 for C > 0). Strict concavity is precisely the mathematical content of “each additional unit of intake raises serum cholesterol less at higher baseline intake,” so the reason→conclusion link is definitional, not merely suggestive. The two worked increments check arithmetically: 1.5·(√200 − √100) = 1.5·(14.142 − 10) = 6.21 vs 1.5·(√500 − √400) = 1.5·(22.361 − 20) = 3.54 — same 100-unit increment yields a smaller rise at higher baseline, confirming the monotone-decreasing marginal. The trailing “at habitual intakes the marginal effect is therefore small” is a weaker quantitative rider that also survives: plugging habitual C into 0.75/√C gives a modest per-unit slope, and even a discrete egg-sized jump reads through the concave form as a diminished increment. No undercutting defeater breaks the concavity→diminishing-returns step conditional on the fitted form (whether the √-form is the true dose-response is a premise-truth question priced downstream, not a validity issue). Holds as stated.