Chapter 4
From Equations to Invariants

All scientific models depend on deeper structural assumptions.
When those foundations are unclear, theories grow complex while their stability weakens.

Understanding the foundations of reasoning allows physics to be rebuilt on coherent structure.

Physical theories describe behaviour, but they rarely explain the structures that allow description itself. Before space, time, or matter can be modelled, a logical framework must exist.

This chapter explores the pre-physical structures that make physics possible.

Modern theories often begin by assuming the dimensional structure of the universe.
When dimensions are postulated rather than derived, deeper inconsistencies can emerge.

This chapter examines why dimensionality must arise from structure rather than assumption.