{"scope":"Elementary independent checks of printed substitutions and the insufficiency of one number expectation for state recovery. No full theory validation.","source":"https://doi.org/10.1007/s10714-026-03528-z","inputs_GeV":{"v":246,"M_Pl":1.22e+19},"calculation":{"x":2.016393442622951e-17,"S_B8":"pi*x**3/3","S_B9_using_stated_relation":"4*pi*x**4","ratio":"1/(12*x)"},"result_ratio":4132791327913279.0,"equality_condition_nonzero_x":"x=1/12","state_counterexample":{"plus":"(ket0+ket1)/sqrt(2)","minus":"(ket0-ket1)/sqrt(2)","overlap":0,"number_expectation_each":0.5,"conclusion":"Equal number expectations do not determine relative phase or the quantum state."},"status":"Issue requiring clarification; no author response requested or received in this task."}