Axioms

Truth is not a primitive term, not a presupposition, and not an axiom. Any definition, proof, denial, or assertion already depends on truth being operative. You can't define it — the definition uses truth to work. You can't assert it as an axiom — assertions are truth-claims. You can't presuppose it — presuppositions are inside the system, and truth is what the system stands on.

The framework can point to this floor. It cannot descend below it. What is beneath — God as the uncaused source of Truth, the rational ground — is where theology does its work from the outside. The socket is mathematics. The plug is theology. The fit is evidence, not proof.

The most irreducible claim. Not provable from inside the system — any attempt to prove it already presupposes existence. Used by everything above it but not itself derived from anything.

The capacity for difference. Without distinction, nothing can be said about anything — every statement collapses into sameness. Like Existence, it cannot be defined without using the concept itself.

Not defined from scratch here — it follows from Existence and Distinction being real. If things exist and can differ, then distinguishable states exist. Information is what you have when distinction is real. (Also appears as Definition D1.1 once formalized.)

The first move of the chain: reality is not an undifferentiated void. Something exists, and that something has internal structure — distinguishable states. This commits the system to an information-bearing reality rather than a contentless plenum.

The information substrate cannot float without support. Any finite grounding leads to infinite regress unless the substrate can ground itself. The Logos field is asserted as self-grounding: it does not require external support because its existence conditions are internal to its own structure. This is the Logos of John 1:1 — identified not theologically here but structurally.

Quantum mechanics makes observation non-trivial: a state in superposition is not actualized until observed. The Von Neumann chain — the regress of observers observing observers — must terminate somewhere. It cannot terminate in a finite observer without circularity. The chain terminates in a terminal infinite observer. This is the structural position identified theologically as God.

Moral orientation is not a continuous variable that can be gradually improved. It is a sign. And like a sign in linear algebra, it cannot be flipped by operations that originate from within the signed system. A negative vector multiplied by any self-unitary operation remains negative. The sign can only be flipped by an external operator. This is the Fall: not a moral metaphor but a structural description of sign conservation.

If identity is information, and information is conserved (not destroyed), then personal identity survives physical transformation. Resurrection is therefore a coherent claim — not magic, but information restoration. Spiritual warfare names something more than thermodynamic decay: active agents working against coherence, not just entropy running its course.

This is where the chain closes. Works-based salvation is ruled out by linear algebra (sign conservation). The Pelagian claim — that humans can self-generate righteousness — is not a theological dispute here; it is dismissed by the mathematics of unitary operations. External grace is not theology added to physics. It is the existence condition for a non-trivial outcome.