Cosmology from Two Axioms 17: Spectral Chain Dynamics Driven by Information Potential Difference and Testable Predictions

Based on twominimalist axioms—information conservation and computability—this paper constructs a self-consistent theoretical framework for cosmology. Theaxiom of information conservation requires that the total von Neumann entropy ofa closed system remains invariant, while the axiom of computability stipulates thatany physical evolution can be simulated by a universal quantum Turing machinewithin a finite number of steps. On the basis of these axioms, we introduce information potential difference as the core order parameter driving hierarchical systemevolution and prove that its minimum unit is ln2. The system evolution manifestsas a series of discrete semantic layers. When the cumulative information torsionreaches a critical threshold of 83ln2, a first-order phase transition occurs, givingrise to a stable four-dimensional spacetime and causal structure. This frameworknaturally corresponds to spectral triples in noncommutative geometry: semanticlayers can be viewed as algebraic towers in spectral chains, the operator realization of information potential difference corresponds to spectral defects, and theself-referential closure dynamics converges to the fixed point of Ricci flow in thecontinuous limit. From this, a series of testable cosmological predictions are derived, including the power-law evolution of the cosmological constant with the scalefactor (exponent α ≈ 1.52), the local-type primordial non-Gaussianity parameterfNL ≈ −3.2, the current value of the dark energy equation of state w0 ≈ −0.992and its evolution rate wa ≈ 0.0083, as well as characteristic oscillations in the primordial gravitational wave power spectrum. These predictions are consistent withcurrent observational data and will be tested in next-generation cosmological experiments (CMB-S4, LISA, SKA-2, etc.). This work suggests that information andcomputational principles may provide a unified dynamical foundation for quantumgravity and cosmology.