Check Mate Atheists, You're All Wrong

[Dystopia]

found your thread interesting and the categories you listed intriguing, however why complicate definitions and classifications so much? Why create new categories when you already have the classic?:
1 - Agnostic atheist 2 - Agnostic Theist 3 - Gnostic Atheist 4 - Gnostic theist (theism also includes deism or pantheism)

As for your equations, I suck at solving and understanding them so I'll ignore that part, I hope it's ok.

Non-Believer: Has no belief or rejects beliefs, such as atheism. Or refuses to believe either way entirely such as agnostic.

That's an agnostic or gnostic atheist, why complicate? We are all non believers to an extend, for instance a Christian is a non believer to all other religions

Non-believer hopeful: A non-believer in a constant state of "soul searching" or spirituality whether it be compulsive or impulsive.

That's not a true non believer, probably some kind of deist who lacks interest in any religion

Belief dissonant: This is the umbrella term for those who bounce between belief and non-belief, and those with a "melting pot," "cafeteria/buffet" conglomerate of diverse belief but never self identifies as anything, but good easily identify with other superstitious persons. Also, this may include social chameleons.

This is a temporary state of reflection, you'll eventually have to decide yourself, there is no such thing as 'absence of belief', you'll have to possess an opinion, even if you're an apatheist

Belief Opportunist: This person is normally self centered and apathetic and may even have a narcissistic personality disorder and because of the ego-driven personality, the person will hold no interest in the certainty or validity of any belief, but chose one where he/she can take personal advantage, substantial gain, power, or leverage.

Then they are not real believers and the category becomes irrelevant

Believe-Doubter: This is an individual that has either been given the culture, environmental, and parental guidance or specific life even pattern that has edged this person into a specific belief in which he/she identifies but is still not satisfied with. This person, like the non-believer hopeful, may be compulsive or impulsive in his/her search for higher knowledge.

You'll eventually decide yourself on the preferable position but you'll always have a defined belief. For example a Christian who starts doubting is no longer a full Christian but can continue being an agnostic theist

Believer- This individual may have times of frequent or infrequent doubt or critique, but will never take the leap to make the cultural plunge or to be involved in further investigation. Granted certain circumstances, this individual may never be confronted with doubt or critical thought, but may without resistance, live fully immersed in belief and belief culture.

Gnostic or agnostic theist.