The Origin and Necessity of Cosmic Quantization

Previous work (Chen, 2026b) established the uniqueness of cosmic presentness and stipulated that the single-step state difference is physically semantically indivisible (Axiom 6), but did not prove why the values of such changes must be discrete. This paper rigorously fills that gap. We first define the Meta-Quantity: the change in any target quantity between two adjacent meta-instants. The meta-quantity is a general concept — it can delineate arbitrary target sets (a single lattice point, a particle cluster, a subsystem) and focus on arbitrary combinations of attribute dimensions (single-dimensional or multi-dimensional). On this basis, we prove three core theorems: Theorem 1 (Discreteness of Meta-Quantity Values and Non-Zero Infimum): From the finiteness of the universe's total information capacity N, it follows that each lattice point's accessible value domain V is finite, and consequently the set of norm-values of any meta-quantity Δq, denoted Λ_step, is a finite discrete set with a non-zero infimum ϵ_min > 0. Any change smaller than ϵ_min would require a continuum state space, violating finite information capacity. Theorem 2 (Indivisibility of the Meta-Quantity as an Atomic Token): Any single-step meta-quantity Δ_q^(k) is a single complete token in physical semantics. Even if its numerical norm bears a multiplicative relation to ϵ_min, that relation is merely a ratio on the real-number axis and does not signify that the physical process consists of multiple sub-transitions. Λ_step is not additively closed. Theorem 3 (The Positive/Negative/Zero Triad Constitutes a Complete Spectrum of Change): Under any observational projection, the sign of any meta-quantity must be positive, negative, or zero; the three jointly form a closed and complete classification of change. Final Conclusion: The values of the universe's underlying changes are necessarily discrete (quantized), and there exists a non-zero minimum scale ϵ_min. Quantization is not a physical assumption, but a logical necessity arising from the joint action of finite information capacity and meta-instant atomicity. Macroscopic continuity arises from coarse-grained averaging.