PAPER-FBT01B: The Four Tension Gates: Structural Origin, Gate Algebra, and Geometric Roles

The four tension gates {X, Y, Z, S} provide the minimal operational skeleton of the Fracture–Berry–Tension (FBT) framework. Their role is not to replace later physical constructions, but to furnish a common structural layer from which later developments drawtheir admissible generators and geometric constraints. In this paper we isolate and organise three basic questions: (1) the origin of the four gates from the first-principle tension structure together with the compressed six-dimensional symplectic geometry; (2) the gate algebra su(2)⊕u(1); and (3) the geometric separation between the non-central horizontal sector and the observable residual vertical sector, including its relation to the three-κ invariant system. The emphasis of the present paper is structural: we identify what is established at the level of gate construction and geometric organisation, while leaving later module-specific gauge and dynamical realisations to subsequent works. The result is a consolidated reference for the four-gate layer within the FBT series.