Dimensional Analysis in Finite Ring Cosmology

This paper explores the role of dimensional analysis as the fundamental grammar that decides which physical expressions can be meaningfully compared before any dynamics is established. We develop this grammar inside the Finite Ring Cosmology framework. In this setting, spatial and temporal dimensions arise as frame readings of a finite symmetry space of admissible reference frames, while conventional units such as metres and seconds enter as observer-assigned modular domains. The shell structure itself is invariant under changes of observer frame and unit convention, although its numerical values change with the chosen scale. The resulting unit-domain algebra reproduces the familiar rules of dimensional analysis: quantities can be added only within the same domain, products and ratios move between domains, and physical invariants are precisely the expressions with neutral total domain. The construction gives a finite-domain reading of the constants that connect mechanics, quantum phase, and gravitation. The speed of light appears as a finite, observer-invariant upper boundary relating spatial and temporal scale assignments: its numerical value changes with units, but the boundary does not. The Planck relation forces energy to share the temporal recurrence domain: h converts frequency measured relative to the chosen time scale into frequency measured relative to the complete phase cycle, not into a separate modular unit domain. The mass domain is derived from energy and speed, and Newton’s constant is identified as the conversion domain for gravitational geometry.