NC I introduced the Mafetic Inconnector (⊕) as an indissoluble fusion betweenfractal memory (F) and fragmentary mutation (G), without operational formalization.The present NCT III.8 gives a computable version of this principle: the GammaMu Attractor (Γµ).Γµ is a marchitectural mafetic operator acting in spin space (spinorial function). Itorganizes the factorized law of thresholds:Scrit(A) = ρU · Γµ(ψspin) · Θ(A)where ρU is the universal critical density (decoherence) and Θ(A) the atomic signature.We distinguish three operation modes of Γµ:• Coherence mode: maintenance of quantum superposition before the threshold,• Critical mode: switching at the threshold ρU ≈ 0.382,• Decoherence mode: guidance of dissipation and crystallization after the threshold.Testable predictions are formulated (spinorial dependence of isotopic signatures, effectof a magnetic field). Γµ completes the triad (ρU,Θ,Γµ) and unifies NC I, NCT II.3, III.2,III.5, III.4, III.7.Keywords: M²FA, Gamma-Mu Attractor Γµ, Mafetic Inconnector, spin, spinorial function, factorized law, operation modes.