Alfic Algebra II The Linear Equation: Image, Point and Completion

This paper extends Alfic Algebra (Paper I, DOI: 10.5281/zenodo.19651215) to equations with unknowns. Building exclusively on the foundational transformation x = x−1, we formulate the Alfic linear equation by replacing the classical zero with the Alfic point b = b−1, grounded in the principle that a point is a real structural unit — not nothing. We introduce the Completion Principle: when an equation reveals that the Image is fractional, the system self-corrects by adding a = a−1 — the same foundational tool the system is built on. No rule is imported from outside the system. The line segment serves as an illustrative example of an abstract mathematical system that extends beyond geometric applications.