Appendix E, Lemma
15 (p. 38): center value
(2 beta q_t + 1-2 beta)/(1+q_t L_t) →
lambda=1/(1+L_t). Here beta is each known
type’s population mass, q_t the center utility ratio,
L_t the pivot’s utility-ratio sum, x_t the
known type’s pivot allocation, and z_t the cold-start
type’s normalized center allocation. At the center, q_t=1/2
and z_t=1; both mirrored known types contribute, giving
lambda=4 beta q_t x_t+(1-2 beta)z_t=1-lambda L_t, using
x_t=1-lambda L_t/(2 beta).
With n=3 items, beta=2/5,
q_t=1/2, and L_t=4/3, the corrected value is
3/7, while the printed expression is 9/25. The
correction affects this center display.