The Standard Model Lagrangian from the Cohesion Unified Field Theory

The Standard Model Lagrangian LSM = Lgauge+Lfermion+LHiggs+LYukawa is assembledhere from the results of the preceding papers in this series. Each sector has a geometricorigin in the Cohesion Unified Field Theory recursion field. The gauge sector (Lgauge) isthe energy density of the torsion phase connection fields derived in the gauge structurepaper. The fermion sector (Lfermion) is the gauge-covariant Dirac equation from theDirac and gauge structure papers. The Higgs sector (LHiggs) is the new contributionof this paper: the Higgs field is identified as the phase separation order parameterof the recursion medium, Φ ∝ ∆R(Dst) = R(Dst) − R0. The Mexican hat potentialV (Φ) = −µ2|Φ|2 + λ|Φ|4is the energy of the recursion medium as a function of itsdeparture from electroweak phase equilibrium. The Yukawa sector (LYukawa) couples thefermion torsion interval structure to the phase separation order parameter, generatingfermion masses. The hierarchy problem — why the Higgs mass is not driven to thePlanck scale by radiative corrections — dissolves in the Cohesion UFT: the Higgs fieldis not a fundamental scalar but the phase separation of the recursion medium, and µ2isthe geometric curvature of R(Dst) at the electroweak density threshold, not a parametersubject to radiative corrections. The Standard Model provides the precise quantitativedescription of all particle physics; the Cohesion UFT provides the geometric substratefrom which the Lagrangian structure emerges.