This seems very different from your earlier explanation. Earlier you explained that all claims to knowledge were ultimately falsifiable under poppers explanation. Now only external are?
The framework of knowledge we had been using was centered around knowledge of reality as a representation between the subject and that which is observed. Also we are talking about justifications thus external reasons to hold a view. This is always falsifiable since our tools and senses are limited. We can have a high probability supporting a representation not 100% certainty. An internal, mental state, is something we can express but never represent as objective knowledge. It is not relational between a subject and that which observed. Thus mental states become subjective knowledge which can only be contained within 1 of the 3 worlds. You nor I can get into minds not our own to verify these mental states.
So it depends if you view your own mental states as knowledge. Do you know you exist or do you believe you exist? Do you know what your own thoughts are or do you believe you do? Do you know your thoughts are your own or do you believe the thoughts are? Keep in mind a belief can be wrong. So if you believe you are acknowledging there is a possibility that your thoughts are produced by someone or something else. Self becomes an illusion. Matrix or brain in a jar.
It would be easier to explain Popper's model.
World 1 is reality, what exists, ultimate truth, etc. It exists regardless of beliefs, claims or self. For example H2O as an atomic structure, this is a reality. World 1 creates World 2 by necessity. If there is no reality there is no person or self.
World 2 is perception, self, mental states, mental processes, consciousness, beliefs, etc. Emotions are mental states. The knowledge of self is personal/subjective knowledge rather than objective knowledge. We can not confirm self by any objective standard. World 2 attempts to understand World 1 which creates World 3. We create hypothesis within World 2 which represent World 1. Science, philosophy, religion, etc are all products of World 2.
World 3 is comprised of representations of communication methods for ideas produced by World 2 representing World 1. The language we are using, the form of the communication, the references used are all forms of communication. We are using World 3 more than World 1 or 2 at the moment
The test/observe line is falsifiability tests and evidence. Ideas which are unfalsifiable as contained in Word 2. Ideas which have a higher degree of probability and have not been falsified yet. These forms into knowledge which is contained in World 3. For example Evolution would be objective knowledge. However objective knowledge is never absolute since it doe not use strict deductive logic.
There are a few points I have skipped covering the links between the worlds. If you are interested I can cover these later. However I think a few of these methods can be deducted easily if you think about the relational stances between worlds along with my bike example and what knowing how to ride a bike entails.