Emergent Mass and Coupling Ratios from Resonant Knot Solitons in R-Theory (Work Model) Methods + Results

This record provides the reproducibility-focused methods companion to the R-Theory work model Emergent Mass and Coupling Ratios from Resonant Knot Solitons. The central idea is that particle-like objects can be modeled as topologically stabilized knot solitons (“Hopfions”) of a coherence order parameter representing the zero-field (𝕆). In this framework, rest mass is identified with the minimum static energy in a topological sector Q, so that dimensionless mass ratios (e.g., E_Q/E_1) and operational coupling proxies can emerge without inserting particle masses or force strengths as independent inputs. Version v1.1 adds an implementation-ready Methods section aimed at independent reproduction of the spectrum E_Q and ratio tables once computations are performed. It specifies recommended domain and boundary conditions, lattice discretization choices, gradient-flow minimization, topological monitoring (Hopf-charge tracking), convergence criteria, and a minimal set of visualization outputs for reporting and comparison. Appendices provide implementation-ready functional derivatives and a “parameter discipline” guideline to avoid per-run hand tuning. Keywords: resonance theory; zero-field; coherence field; knot solitons; Hopfions; Skyrme–Faddeev; topological charge; emergent mass; reproducible numerics.