φ-Lattice Extensions: RG Running, Complex A₄, Dark Matter, and Collider Anomalies

This is the second part of the φ-lattice program. Following the successful prediction of all eight SM mixing angles from the A₄ = SU(5) Coxeter matrix, we test whether the same algebraic structure extends to: • RG-running fermion masses — m_s/m_d = λ⁻² = 20 is RG-invariant• Complex A₄ spectrum — A₄ + iκB with κ ≈ 1• Dark matter — FIMP/axion scenarios• Collider anomalies — g-2, K→πνν, LHCb B-anomalies Positive results:• RG-invariance: m_s/m_d = 20 at both 2 GeV and GUT scale• δ_CP improvement: (2π/5)(1+X⁵) = 78.49° (0.73% from PDG)• 0νββ prediction: m_ββ = 0.87-2.34 meV Negative results:• Fermion masses: Monte Carlo p > 0.05 (not φ-lattice)• FIMP dark matter: required α_eff ~ X⁻⁵¹ (not X²)• Axion: required f_a = M_Pl X³¹ (not natural)• g-2 anomaly: no X^n match• LHCb B-anomalies: no X^n match Conclusion: the φ-lattice works for mixing angles but not for masses, dark matter, or collider anomalies. We report these negative results to constrain the scope of the framework. Companion paper: DOI 10.5281/zenodo.22807039