I wish to accomplish this

<div class="postbox format-standard">

without all of this stuff from publish_class(). Any ideas?

Well, this really is mainly wordpress question, since in codex read:

Styles should make use of the publish_class() function within the wrapper code that surrounds the publish to >add dynamic styling classes. Publish formats may cause extra classes to be included this >manner, while using "format-foo" title.

but publish_class() is creating something similar to

class="class-name post post-4564 category-48 hentry format-standard category-dancing logged-in"

that we shouldn't have.

what i believed about is applying get_publish_format() to create publish format with a variable, after which creating dynamic class with this variable.

I do not get why this is inproper, when i thought peolple who are able to assist me to can say for certain wordpress well.