The Global Synchrony of Yuanke and the Ground-State Constant of Xushi ——The Unified Rhythm of Discrete Cosmic Evolution and the Necessary Constant of Imaginary Time

Previous works (Chen, 2026b; Chen, 2026c) established that physical reality exists only in the present Yuanke (the previous instant is inaccessible, the next has notyet arrived), and defined the component of Yuanliang in a single step of evolution:Xushi (the minimum granularity of the corresponding classical “time” variation under observational projection). However, whether the discrete state sequence sharesthe same transition event (Yuanke), and whether Xushi is a global constant, havenot been rigorously demonstrated.This paper constructs a proof system starting from the fundamental principlesthat “every physical evolution must have a source of change” and “Yuanliang fluxconservation.” We first prove that any nonzero evolution of a lattice point mustoriginate from a directly neighboring lattice point under the same evolutionarytransition (the Locality Forcing Lemma); then, from the recursive constraints of aconnected lattice graph and the global definition of the deterministic map, we derivethat all lattice points share a single global transition event (the Global SynchronyTheorem). Subsequently, using only finite information capacity and the singlevaluedness of the deterministic map, we prove that the values of Xushi possess aglobal minimum positive number (the Ground-State Constant Theorem of Xushi),and we argue that this constant is the only reasonable anchor for a macroscopicallyuniform “time” reading.Finally, using information entropy and the Compton scale of elementary particlesas heuristic anchors, we give an order-of-magnitude conjecture of ∆smin ∼ 10−42 s,and provide three independently testable predictions.Correspondence to: [email protected]