First-Principles Derivation of the Ground-State Vacuum Floor Identity: Transitive Inferences on the n = 4 Active Neutrino Soliton in Big Boot Gauge Theory (O ZIP )

In the Standard Model (SM) of particle physics, fermion rest masses are introduced asempirical parameters via arbitrary Yukawa couplings to an unquantized scalar Higgs field.Moreover, the origin of non-zero active neutrino rest masses (mν> 0) remains a core puzzle,typically requiring ad-hoc high-energy mechanisms such as the Type-I/II Seesaw mechanism(∼ 10^14GeV). In this paper, we employ transitive logical inference within Big Boot GaugeTheory (BBGT) and Octonionic ZIP Algebra (OZIP) to demonstrate that the active neutrinomass scale (mν≈ 0.05838 eV) is a direct, first-principles identity emerging from the n = 4ground-state projection floor. We prove that at the n = 4 level channel, the Master MassSpectrum Operator (MˆBBGT) acts as the identity operator (MˆBBGT≡ I), as the nonassociative associator torque (Aassoc) and M¨obius graph topological curvature (∆M¨obius)identically vanish (∆M¨obius + A assoc⃓ n=4= 0). Consequently, the active neutrino is revealedto be the unique ”naked” zero-mode soliton in nature—an unperturbed vacuum projectionof the substrate fine-structure constant (mν= 8α · 1 eV ≈ 0.05838 eV). Furthermore,we outline the theoretical implications, quantum technological applications, experimentalbreakthroughs, and falsifiable predictions implied by this zero-torque ground-state identity