Entropic Time Against the Clock-Assignment Rule: The Laboratory Construction Is the Screen's Compliant Case — and Not a Cosmological Clock

Reads Barontini's entropic time (Phys. Rev. Research 8, L022047: time assigned from the bright sector's distribution change in a sealed 24,000-atom system; time stops where the distribution stops changing) against the Clock-Assignment Screen's stated rule (a clock claim must output d(tau)/dt from stated clock physics, and name a separating observable — redshift expressly insufficient). The Screen's priced exhibit is recomputed as the gate (logarithmic assignment: d(tau)/dt = 1000 / 1 / 0.01 at the printed points). Entropic time is then formalised on a declared relaxation: tau_E saturates and d(tau_E)/dt decays to zero exactly where the distribution stops changing — the paper's printed behaviour falling out of the assignment's definition. Clause by clause, the laboratory construction satisfies the Screen's demanded form (assignment output from stated clock physics; separating evidence internal and named: event-ordering and reproduced evolution), so the packet prints the reduction: entropic time is a special case of the compliant assignment class — with the scope difference at full size beside it (single-system laboratory analogue of the Wheeler-DeWitt problem, not a cosmological two-time claim, and not promoted to one). EXTENSION. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.