It was getting dark when Kyon started to study case S-1.
There were two options: either Lindia got pregnant by Stein or someone else.
In the second case, the offender was someone who adored Lindia and who could drug the patriarchs' children. Who was capable of this? No one among Lindia's young fans, that's for sure. Thus, this theory was highly improbable.
What if Lindia got pregnant by Stein. Who was he? A popular 22-year-old guy, the first genius of the empire, an example for the younger generation, the empress' student who didn't show any interest in the opposite sex. What were the odds that he couldn't hold back his lust in front of the weak and clingy Lindia? Hardly any.
Therefore, the patriarchs' children had been drugged with unknown powerful substance as Stein was a peaking king phaser (6). Who might be responsible for this? Who could be capable of this?