Meta-Instant Global Isochronism and the GroundState Constant Theorem

Previous works established the presentmoment uniqueness of physical reality (only the state Uk at the current evolution step k exists) and the essential discreteness of metaquantity values. However, whether there exists a unified and unique logical index for the discrete state sequence, and whether the classical “time” variation corresponding to a single evolution step under observational projection is constant, have not yet been rigorously demonstrated. This paper builds a complete proof system from three fundamental principles: “physical evolution must have a source”, “metaquantity flux conservation”, and the “discrete principle of least action”. First, we prove that any nonzero evolution of a lattice site must originate from a directly neighbouring lattice site in the same evolution step (Locality Forcing Lemma). Second, from the recursive constraints of a connected lattice graph and the global definition of the deterministic map, we derive that the entire universe shares a single global evolutionstep index (Global Isochronism Theorem). Third, by employing the calculus of variations to exclude nonuniform projection measures, and combining this with the deterministic singlevaluedness requirement of a “commanderfree” system, we prove that the imaginarytime step size under observational projection must converge to a global minimum constant (GroundState Constant Theorem). To resolve the semantic contradiction that “time does not exist yet duration does”, we introduce imaginary time s—a logical tool strictly analogous to the imaginary unit i, which has no corresponding storage unit in physical states but mathematically connects discrete metainstants to classical physical observations. Finally, using information entropy and the Compton scale of elementary particles as heuristic anchors, we give a conjectured magnitude Δsmin∼10−42 s and provide three independent testable predictions.Correspondence to: abillchen@126.com