INTERNATIONAL JOURNAL OF PROFESSIONAL STUDIES

This paper develops a compact framework for four-dimensional N=1 F-theory on resolved elliptic Calabi–Yau fourfolds. The discussion starts from the Weierstrass model, keeps track of crepant resolution data, and follows the same classes through the Shioda map, the shifted G?-flux law, tadpole cancellation, matter-surface indices, and residue formulae for holomorphic Yukawa couplings. The main point is that these calculations can be placed in one clean sequence of lattice, Chow-ring, and Deligne-cohomology steps. Within the stated admissible class, the flux set is finite, chiral indices are integral, hypercharge masslessness becomes a lattice condition, and local Yukawa entries reduce to finite residue algebra. The paper also gives worked SU(5), SO(10), Pati–Salam, E?, and abelian-sector computations with diagrams and full reference data.

Keywords: F-theory; Calabi–Yau fourfolds; G?-flux; Shioda maps; singularity resolution; N=1 compactifications; moduli stabilization; swampland; Deligne cohomology; Yukawa couplings.