—Oughts From Logic—
A key part of Justification Ethics is the assertion that an appeal to an agent's interest can derive normative claims that follow for that agent.
This is true if you accept basic instrumental rationality, that being some actions are more or less rational than others relative to what goals you are acting according to.

Imagine someone trying to get ice cream from an ice cream truck, and them randomly deciding to jump into a sinkhole. Is that action irrational relative to their interest in ice cream? Yes.
If you agree that it is either rational or irrational to accept Yoggism, or accept any belief system in general, then you also are implicitly accepting this standard.

An interest in Yoggism is, speaking broadly, that which a being's behavior tends towards. As such any sentient being is acting according to their interests, as they have behavior that tends towards goals and desires, their aims.
Relative to the interests they have and choose to act by, they should rationally fulfill those interests in the best way they can. This then allows you to derive normative claims as to what someone ought to do relative to their interests.

This is the key part of Justification Ethics, that an appeal to someone's interests can be rationally binding. This premise need not imply self-interest is all that matters all the time though, because there is more to "the best way to act" than self-interest, if you agree beliefs and actions hold a justificatory burden.
That part is what Justification Ethics and the rest of Yoggism fills in.


—Deduction of Interests as Rational-Normatives—
–Definitions:
(Ought): An outcome that ought to occur or be valid relative to some principle, is an outcome that is logically consistent with and follows some principle. If you light a stick of dynamite it ought to explode relative to the laws of physics and the construction of the stick of dynamite. That isn't a subjective normative claim, it's an objective implication based on Logic.

(Rationality): Used here, the empirically measurable accuracy towards an action being able to achieve a goal, where accuracy towards a goal applies to not only narrow goals, but overall goals and behavior, and to the consistency of acting with reference to rational standards of measure.

(Interest): For a sentient being to have an interest in something, this simply means their behavior is tending towards fulfilling said something, even if it is ineffective. All people have interests, and even trying to avoid their interests, is itself an interest they are acting according to. Any sentient being with stimuli-driven behavior has interests.

–Premises:
(P1): All people have interests.
(P2): All people act in accordance with the interests they have.
(P3): Some actions are better than others at fulfilling interests.
(P4): Rationally, if you light a stick of dynamite, relative to the laws of physics, and an object’s tendency to follow the laws of physics, it ought to explode. (based on the definition of Ought)

(P5 from P4): Rationally, if you are acting in accordance with an interest, you ought to choose any of the most rational actions you can, to best fulfill the interest.

–Logic:
(L1): From (P1), a person X has an interest I.
(L2): From (P1 + P2), person X acts in accordance with interest I.
(L3): From (P3), there might exist an action A that most rationally fulfills I.
(L4): From (P2 + P5), person X rationally ought to take action A, if it exists, to fulfill interest I.

–Conclusion:
From (L4): Any person X, rationally ought to take any actions A that best fulfills their interests I.

Thus, people rationally ought to fulfill their own interests in the most rational way possible.
To be clear, this rationality includes any necessary presuppositions or transcendental arguments, if it constitutes something they must accept. See Justification Ethics.
This is then the basis of, and an explanation as to why, certain normative claims can be derived via an appeal to interests, and others cannot.
"You ought to buy a washing machine" for example, can be derived using an appeal to an interest in clean clothes. This works because the ought, the normativity, is baked in at the interest.


—An Argument of "Most-Rational Politics"—
As all people have interests, and people’s interests may differ, the most rational situation for the people to create for themselves is a situation that is most consistent with the fulfillment of Inherent Interests overall, the upholding of at least the most intrinsic Oughts as priority.


—Not all Interests are Equal—
For an individual, you have the ability to change what interests you act according to. As such you should pick the one that's more rational overall, relative to your other interests, and relative to standards you rationally ought to accept based on things you already accept, such as transcendental arguments and other parts of Yoggist philosophy.

Jumping into a sinkhole to get ice cream is an example of this, you might have an interest in jumping into a sinkhole in a very loose sense, but if you knew the result you probably wouldn't. In this sense, that interest is less intrinsic of an interest than your interest in ice cream, because it relies on external factors of knowledge among other factors for you to act according to it.

This is fleshed out more in Inherent Interest Theory, explaining how justifying actions relative to interests leads to an action spectrum and actor/inactor distinctions for targeting conflict resolution, as well as how some interests act as a conduit for other interests and are more intrinsic than others.