τ^3 as geometric readout τ^1×_f T^2

The geometric object denoted τ^3 is constructed as a readout of τ, not adopted as a Cartesian product. It is not τ×τ×τ. The base τ^1 is the (D,A) radial/address base of the ABCD chart; the fiber T^2 is the (B,C) solenoidal fiber built from the two bipolar character channels. The fiber map f records the nontrivial dependency, so no global trivialization τ^3≅τ^1× T^2 is asserted. This fibered readout is the canonical geometric body that later becomes the substrate candidate for the Book-III physical carrier.