Bounded Phase Space
Every computation inhabits a bounded coordinate system. Every state has an address. Every trajectory has a destination. This is why the framework has guarantees—not heuristics.
S-Entropy Coordinates
All information in the system is represented as a point in the unit cube S = [0,1]³, with three coordinates:
Total entropy is conserved through every morphism chain. Knowledge gained must come from temporal or evolution entropy reduced. Nothing is created or destroyed—only transformed.
Entropy Conservation in Practice
S-entropy coordinates through the ACTN3 validation: three source extractions followed by two compositions. The total (dashed line) remains constant while individual components redistribute.
Foundational Axioms
Bounded Phase Space
All computational states inhabit S = [0,1]³. There is no state outside the unit cube. This boundedness ensures that every trajectory is finite, every search terminates, and every convergence is measurable.
Triple Equivalence
Three descriptions of the same system—oscillatory, categorical, and partition—yield identical entropy: S = k_B M ln n. Any proof in one description transfers to the others. This is the foundation of cross-modal composition.
Ternary Representation
Memory is addressed in base-3, not base-2. Each trit encodes three states (known, unknown, partially-known) rather than two, yielding 3^k categorical addresses. Information density per digit is maximized at base e ≈ 2.718, making ternary the closest integer optimum.
Categorical Navigation
Movement through phase space follows morphism chains—composable, type-checked transformations that preserve S-entropy conservation. Navigation is not search; it is categorical composition with guarantees.