A Dimensionless Theorem Base in Geometric Algebra for Label Media, Field Equations, de Sitter Space and Galaxy Regularities

We collect one hundred theorems in geometric algebra (GA), each with its premises, the idea of its proof and a computational check. Their outputs are dimensionless, apart from the comparisons with data: exponents, ratios, signs, numbers of degrees of freedom and function shapes. Dimensional numbers (a₀, Λ, H, G, masses) are excluded and classified as values of solutions, constants of the action or scales of a broken dilation, none fixed by symmetry. The base covers matter from volume-preserving relabelling, the selection of field equations, the conformal geometry of de Sitter space, the scaling group of collisionless self-gravity and label media. Further layers give predictions (the S8 line of the dust–scalar coupling, the evolution of the acceleration level, the dust–baryon fall difference) and foundations (signature, horizon equilibrium, half-integer spin). The response of geometry to matter is an independent axiom, replaceable by horizon equilibrium. Nearly all the physics is known; ours are the GA formulation, the dimensionless organisation with explicit hypotheses and the falsification record.