Global Synchrony of Meta-Instants and the Ground-State Constant Theorem

Previous works established the uniqueness of the physical present (only the stateUk at the current evolution step k exists) and the essential discreteness of MetaQuantity values. However, it has not been rigorously demonstrated whether a uniqueand universal logical index exists for the discrete state sequence, nor whether theclassical time variation corresponding to a single evolution step under observationalprojection is constant.Starting from three fundamental principles every physical evolution musthave a source, Meta-Quantity ux conservation, and the discrete least-actionprinciple we construct a complete proof system. First, we prove that any nonzero evolution of a lattice point must originate from a directly adjacent lattice pointat the same evolution step (the Locality Enforcement Lemma). Second, from therecursive constraints of the connected lattice graph and the global de nition of thedeterministic map, we derive that the entire universe shares a single global evolutionstep index (the Global Synchrony Theorem). Third, via a variational method thatexcludes non-uniform projection measures, combined with the deterministic singlevaluedness requirement of a commanderless system, we prove that the imaginarytime step size under observational projection must converge to a global minimumconstant (the Ground-State Constant Theorem). To resolve the semantic paradoxof time does not exist yet duration does exist , we introduce imaginary time s alogical tool strictly analogous to the imaginary unit i, which has no correspondingstorage unit in the physical state but serves as an indispensable mathematical bridgebetween discrete Meta-Instants and classical physical observations. Finally, usinginformation entropy and the Compton scale of elementary particles as heuristic anchors, we give an order-of-magnitude conjecture ∆smin ∼ 10−42 s, along with threeindependently testable predictions.Correspondence to: abillchen@126.com