= Nonreflection of fixed order-type fibers
{title2=$E_\xi=\{\zeta:\operatorname{otp}(C_\zeta)=\xi\}$}
For a coherent <club set> sequence, the limit points of $C_\delta$ form a <club set> whenever $\operatorname{cf}(\delta)>\omega$. Along these points, $\operatorname{otp}(C_\gamma)=\operatorname{otp}(C_\delta\cap\gamma)$ strictly increases, so a fixed fiber $E_\xi$ meets this a <club set> at most once and cannot reflect at $\delta$. Under the <square principle> order-type bound, the fibers with $\xi\le\kappa$ partition all <limit ordinals> below $\kappa^+$ into $\kappa$ non-reflecting pieces.
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