DWTT & GACTP - A Canonical Control Case for Enantiomeric Cancellation

Directed-With-Time Theory (DWTT) is a constrained canonical construction in which a transport scalar T(x) functions as an internal clock only after full Dirac reduction of the Hamiltonian constraint. I develop DWTT in an explicitly textbook canonical form, resolve the two deparameterized clock orientations, σ = ±1, and replace the auxiliary tether sector with a lean DWTT Witness Sector built from a projection field t4(x) and a reaction field μ(x). The analysis is fully explicit (parent action, primary/secondary constraints, reduced clock momentum, regularity domain, and constraint closure). The key point is negative: the Witness Sector refines the regular domain but does not break the branch-exchanging involution. DWTT, therefore, does not locally generate a determinate arrow. This makes DWTT a clean control case and forces the Global Asymmetry for Canonical Time Persistence (GACTP): if the admissible reduced history space is globally invariant under the enantiomeric involution, then every directed temporal ledger has an admissible mirror ledger of opposite sign, and determinate temporal persistence cancels. The missing ingredient is not another local canonical refinement, but a global asymmetry of admissibility.