Chiral Object Formation and CP-Odd Branch Obstruction in the Higgs–Yukawa Sector

This paper develops a categorical-linear interpretation of fermion mass formation and CKM-type CP violation in the Standard Model. The central idea is that a massive fermion is not simply a direct combination of left- and right-chiral components. Before electroweak symmetry breaking, the two chiral sectors are treated as independent pre-objective readings. After the Higgs vacuum is selected, the Yukawa interaction becomes an active boundary relation that allows these two sectors to be coherently joined into a massive Dirac object. In this interpretation, the Higgs vacuum functions as a structural enabling event. It does not merely supply a numerical mass scale; it makes the left-right chiral pairing operationally realizable. A massive fermion is therefore understood as an object formed through compatibility between its left- and right-chiral readings. The paper then applies the same object-formation language to the quark sector. The up-type and down-type mass structures define two distinct branches on the common left-handed flavor space. CKM mixing arises because these two branches cannot, in general, be separated in a single common flavor basis. CP violation appears when this branch separation failure leaves a basis-independent CP-odd residue. Thus, the paper does not propose a new particle, force, or modification of the Standard Model. Its contribution is interpretive and structural: fermion mass is described as chiral object formation through a Higgs-enabled boundary relation, while CKM CP violation is described as the invariant residue of a three-generation branch obstruction.