5 Proposition 1.6.4 and Corollary 1.6.5

This chapter assembles the headline theorems of the project: Stanley’s Proposition 1.6.4 (EC1 p. 60) — proper containment of omega-sets forces strict inequality of \(\beta \) — and the immediate corollary Corollary 1.6.5 (EC1 p. 61) — the alternating descent set strictly maximizes \(\beta \). Both are kernel-checked, axiom-free, and closed under the global context.