In Neal Stephenson's Anathem, the gates of Unarian, Decenarian, Centenarian and Millenarian maths open once a year, decade, century and millennium respectively. But what is the Day Gate for? Clearly, avout cannot go out the Day Gate. But extramuros are allowed in and even allowed to interact with Decenarians. This being the case, how is the separation from extramuros maintained?

In Neal Stephenson's Anathem, the gates of Unarian, Decenarian, Centenarian and Millenarian maths open once a year, decade, century and millennium respectively. But what is the Day Gate for? Clearly, avout cannot go out the Day Gate. But extramuros are allowed in and even allowed to interact with Decenarians. This being the case, how is the separation from extramuros maintained?

Update: When I say avout, I'm not including the hierarchs, who interact with the Saecular World. And when I say extramuos, I'm not including the officials that the hierarchs may interact with. Specifically, how could people like Flec and Quin be allowed through the Day Gate and talk to Tenners such as Orolo and Erasmas?