Fractal Minimal Inconsistency Background and the Matter-Antimatter Asymmetry

The observed dominance of matter over antimatter remains one of the central open problems of early-universe physics. This paper develops a publication-oriented formulation of a Fractal Minimal Inconsistency Background (FMIB) within the broader Fractal Consistency Law (FCL) and Principle of Minimum Inconsistency (PMI) program. The central claim is deliberately modest but technically precise: if the universe is governed by a tendency to minimize structural inconsistency, then a small, dynamically evolving fractal background can act as an effective bias in baryon or lepton number generation while also producing controlled perturbations of the cosmological expansion history. We first reconstruct the integral FCL-PMI framework and clarify how the PMI can be cast as a variational principle. We then provide two concrete field-theoretic realizations: a Standard Model plus FMIB derivative coupling to the baryon current in the presence of baryon-number-violating operators, and a minimal fractalized leptogenesis sector with heavy Majorana neutrinos. These constructions identify explicitly where baryon or lepton number violation, CP violation, and departure from equilibrium enter at the Lagrangian level. We next present a toy Boltzmann benchmark showing that a fractal bias parameter of order LambdaF = 4. 45e-7 reproduces the observed baryon-to-photon ratio eta = 6. 0e-10. We also specify a broken-power-law stochastic gravitational-wave template associated with an FMIB transition. Finally, we implement a localized Gaussian deformation of H (z) in a modified CLASS background code and compare it against an independent vanilla CLASS run. The resulting ratio HFMIB/HLCDM - 1 exhibits a clean Gaussian bump with peak amplitude 9. 9998e-4, validating the implementation at the 10^-3 level. The paper does not claim empirical confirmation of FCL; rather, it establishes a coherent mathematical, numerical, and computational scaffold through which the FCL-PMI program can be confronted with baryogenesis, gravitational-wave, CMB, BAO, and large-scale-structure data.