Emergent Time from Barrier Iteration (Reduced Form)

T65 develops an emergent effective-time framework for the reduced Q5 transport architecture. The theorem interprets repeated admissible barrier transport steps as a discrete iterative evolution process and introduces a coarse-grained effective time parameter=n, \ (n\) counts admissible transport iterations and \ (\) is the effective iteration scale. The resulting reduced evolution operator takes the form₄₅₅=e^-i H₄₅₅, the reduced generator structure emerging through the mediated reduction chain AL=iK^ AL K_. theorem, therefore, establishes that the observable reduced rotational dynamics arise through mediated admissibility reduction rather than direct projection from the original transport generator. T65 is structurally important because it reframes the reduced rotational invariant \ (\) as part of an effective iterative evolution system on the reduced defect sector. The theorem further demonstrates, through explicit second-order mediated calculations, that antisymmetric rotational structure emerges dynamically from leakage-sector circulation. The resulting effective-time parameter is a coarse-grained description of repeated admissible transport evolution rather than a derivation of fundamental physical time. Reversibility remains preserved at the operator level, and no intrinsic thermodynamic arrow of time is claimed. Status: solid for the effective iterative evolution structure and mediated reduced-generator construction under the stated reduction assumptions; conditional on the effective-unitary embedding and global closure properties of the reduced evolution operator; speculative for any identification with fundamental physical time or irreversible temporal dynamics.