Canonical Projection of Raw Barrier Transport onto Reduced Phase Transport

T81 establishes the canonical projection of the raw Q5 barrier transport operator onto the reduced phase transport sector. The theorem begins from the first-order raw transport expansion\[Traw=I+1/160A+Sₙᵣ+O(ε^2),\]where\[A=iσ_y,^2=-I,\]and\[Sₙᵣ\]is symmetric/scalar non-rotational dressing arising from the paired transport structure identified in T48. T81 proves that raw purity is false:\[Sₙᵣ ≠ 0\]in general. The correct structural statement is instead that the canonical phase-readout projection induced by the T26-T29 extraction pipeline kills the non-rotational dressing:\[Pₚₕₐₛₑ(Traw)=I+1/160A+O(ε^2)=Tₚₕₐₛₑ.\] Equivalently,\[Traw=N_ε · Tₚₕₐₛₑ+O(ε^2),\]where\[N_ε=I+Sₙᵣ\]is projection-null symmetric/scalar dressing invisible to the phase-readout sector. The theorem is structurally important because it closes the open gap identified in T80. The continuous phase-flow result\[Tₚₕₐₛₑ^ktA\]no longer depends on manually removing unwanted operator dressing by hand. The T26-T29 extraction architecture canonically projects onto the rotational transport sector from first principles. T81 also marks a conceptual shift in the framework: observable structure is not identified with the full raw operator but with the projection-defined observable sector of a richer transport architecture. The theorem therefore replaces earlier implicit “raw purity” assumptions with observable-sector equivalence under canonical projection. The non-rotational dressing lies in the null-class operator sector\[span\{I,σ_z,σ_x\},\]while the rotational component\[1/160A\]survives the projection uniquely. Status: solid for the projection-null structure of the non-rotational dressing under the T26-T29 extraction pipeline and for the canonical reduction\[Pₚₕₐₛₑ(Traw)=Tₚₕₐₛₑ;\]conditional for the near-identity crossing model inherited from T48-T49 and for extension beyond the reduced defect-sector transport plane.