Particle Mass Framework Derived In Recognition Science

In the Standard Model, fermion masses are free parameters encoded by Yukawa couplings to the Higgs field. This paper develops an alternative ontology of mass within Recognition Science (RS), a framework in which all physical structure is derived from a single functional equation—the Recognition Composition Law. We show that mass emerges as a geometric property of recognition boundaries: self-sustaining patterns on a discrete ledger whose persistence is governed by cost minimization. The unique cost functional $J(x) = \frac{1}{2}(x+x^{-1})-1$, forced by the Recognition Composition Law together with normalization and calibration, selects the golden ratio $\phi = (1+\sqrt{5})/2$ as the unique self-similar scaling base. Mass hierarchies are encoded by integer positions on a $\phi$-ladder, while sector-level scales are fixed by cube combinatorics (D=3). We derive the recognition operator $\hat{R}$ that replaces the Hamiltonian, show how the eight-tick closure cycle ($2^{3} = 8$) provides a canonical period, and demonstrate that interactions between recognition boundaries reduce to cost-weighted adjacency moves on the cubic ledger. The Higgs mechanism is reinterpreted as the low-energy effective description of a fundamentally discrete process. Companion papers develop phenomenological predictions (II), the neutrino sector (III), transport discipline (IV), the fine-structure constant (V), and the generation problem (VI).