Definitions

The foundational definition. Follows directly from Existence and Distinction (the Level 0 primitives). If things exist and can differ, information exists. Shannon entropy formalizes this: H(X) = −Σ p(x) log p(x). This definition makes information ontologically basic rather than derivative.

Good is not defined morally first and then argued to physics. It is defined structurally: an action or state is good if it increases the coherence alignment score. This definition allows moral physics to run without circular appeal to intuition.

High coherence means the system's internal structure mirrors the rational order of the Logos field. Low coherence means the system fragments — more entropy, less integration, less capacity to maintain complex order. The gradient dC/dt is the moral physics analog of thermodynamic flow.

The Logos field is not derived from physical matter; physical matter is a subset of its distinguishable states. It is self-sustaining in the sense that its existence conditions are internal to its own structure, unlike any finite substrate. Named Logos after John 1:1 as a theological identification, not a theological derivation.

Moral orientation is modeled as a sign, not a spectrum. σ = +1 indicates alignment with the Logos; σ = −1 indicates opposition. The sign is conserved under self-operations (the Sign Conservation Theorem T8.1). Only an external non-unitary operator can flip it.

χ is what the system is tracking: the overall coherence trajectory of a person, community, or physical system. The Master Equation computes χ by integrating ten contributing variables across space, time, and soul. Understanding what drives χ — and why external grace is required for χ > 0 as t → ∞ — is the core question the framework answers.

Non-unitary: it changes the norm (the "size") of the state vector, not just its direction. That is what makes sign-flip possible — unitary operators preserve norm and therefore preserve sign.

External: it cannot be self-generated. A system cannot pull itself up by its own bootstraps. The Grace Operator entering from outside is the formal analog of what theology calls grace.

The standard information-theoretic entropy measure. Used in the framework to quantify disorder in moral and physical systems alike. The second law drives H(X) upward in closed systems, which is why η_S (the entropy variable in the Master Equation) tends toward zero without external input.

The coupling function determines how strongly grace connects to a given soul state. BC8 (Voluntary Coupling) constrains V(Ψ): the coupling must be voluntary, not coercive. Grace is offered; the coupling requires free response. This is not a theological add-on but a structural requirement of the formalism.