The RFW Orthotope: A Sandbox Phenomenological Model for Fermion Mass and Charge Discretization

While the Standard Model successfully describes fermion interactions, it lacks fundamental theoretical explanations for the free parameters in the fermion mass spectrum, the fractional charges of quarks, and the origin of the three fermion generations. Within the Higgs--Yukawa framework, this paper proposes a three‑dimensional RFW (Ren‑Fuwen) Ortho‑Body, a self‑similar geometric heuristic sandbox phenomenological model, to \textbf{provide a heuristic algebraic‑geometric picture} for the mass spectrum and charge spectrum of fermions. The model is defined solely by spatial dimensionality $N=3$, contains no continuously tunable free parameters, and incorporates discrete geometric postulates. A complete Lagrangian formulation for quantum field theory is not yet established. On geometric grounds, based on the moment of inertia of the RFW‑Orthotope, an algebraic framework over the finite field $\mathbb{F}_{7}$ is adopted, yielding three disjoint coset orbits. Two discrete geometric postulates are imposed to select twelve stable hinge‑point quantum $k$-values. Substituting these into the mass‑mapping geometric postulate gives twelve stable energy states. These twelve states are uniformly distributed over the three coset orbits, with four states per orbit. For the mass spectrum, comparing this algebraic structure against PDG 2024 fermion data shows that nine energy states \textbf{reproduce} the masses of the nine charged fermions, and the algebraic structure \textbf{reproduces} the three‑generation pattern of fermions. The remaining three states, with masses 540 MeV, 270 MeV, and 2.66 MeV, are orbit companions output algebraically by the model. According to the charge‑mapping logic of the present model, hinge‑point configurations carry non‑zero effective charge; however, their full quantum numbers and couplings remain unconstrained. Regarding falsifiability, the charged‑fermion mass formula is heuristically extended to neutrinos. Using neutrino‑oscillation experimental mass‑squared differences as constraints, the model yields \textbf{conditional} neutrino‑mass predictions: $4.988 \times 10^{-2}\,\text{eV}$, $9.897 \times 10^{-3}\,\text{eV}$, and $4.948 \times 10^{-3}\,\text{eV}$. The model favors the normal mass ordering. The summed neutrino mass $\sum m_{\nu} \approx 0.065\,\text{eV}$ satisfies cosmological upper bounds. Within the scanning window, the stability rate of solutions under $1\sigma$ uncertainties reaches 95.2\%. These predictions serve as conditionally falsifiable clues to be tested by future experiments. At the electroweak spectral level, under the mapping assumptions of this work, the set of three‑string rotational difference moments of inertia can \textbf{reproduce} the fractional charges of the nine charged fermions (six quarks and three charged leptons) as well as their antiparticles. Weak hypercharge is computed using Standard‑Model electroweak relations. This model stays inside the Standard‑Model framework. It does not modify well‑established Higgs mechanism and electrodynamics. It merely explores the origin of Yukawa couplings, generation structure, and fractional charges via heuristic discrete‑geometric reasoning.This work mainly reports this intriguing mapping phenomenon; we encourage the community to further investigate its underlying deeper‑level dynamical principles.