Continuum Limit and Effective Field Description from Doubled-Sector Mass Pairing in Finite Reversible Closure - Paper 15

Continuum Limit and Effective Field Description from Doubled-Sector Mass Pairing in Finite Reversible Closure - Paper 15 ABSTRACT Paper 14 established that isotropic first-order propagation in three spatial dimensions requires representation enlargement to four components and that lattice admissibility supplies paired low-energy sectors (doubling). The deferred step was the explicit construction of the anticommuting mass operator from these doubled modes. Paper 15 constructs that operator directly as a strictly local sector-pairing map and then performs the controlled long-wavelength limit of the composite excitation sector. Using only finite reversible closure, locality, translation invariance, the linear infrared dispersion branch and the induced Z2 grading from the composite holonomy sector, we obtain an infrared effective action of Dirac-type at the level of operator algebra. No appeal to continuum Lorentz symmetry is used. Isotropic scalar closure is the only symmetry input. Parameters (c, m) are mapped explicitly to lattice observables. INTRODUCTION The Finite Reversible Closure (FRC) programme builds physical structure from strictly local, finite-dimensional reversible update. Paper 10 constructed a gauge-invariant composite excitation.Paper 11 derived Z2 parity.Paper 12 operationalised involutive holonomy.Paper 13a showed that non-commuting transport algebra forces a two-component structure.Paper 13b demonstrated that a linear infrared dispersion branch forces a first-order kinetic operator.Paper 14 proved that isotropic scalar closure in three spatial dimensions requires four components and identified lattice doubling as the partner space required for mass completion. Paper 15 executes the remaining structural step: Construct explicitly the anticommuting mass operator from doubled low-energy sectors and derive the infrared effective action. No new assumptions are introduced. All inputs come from Papers 10–14.