AbstractVolume IV completes the theoretical foundation of the Cohesion Monism (CM) by resolving the paradoxicalboundary conditions of Evolutionary Compression (EC). The origin point is defined as the InformationalSingularity (Σ): a state of Maximal Symmetric Informational Potential where Statistical Complexity (SC =0) due to perfect symmetry. The core mechanism is the Rg Conservation Principle, which states that thetotal coherence (Rg) is conserved by the topological structure of the manifold. This principle manifestsas the Coherence Constraint (Cco), which is the inherent topological law preventing EC from reaching theZero-Bound (Z −B) (the collapse to a non-compact, trivial manifold). The Cco thus solves the CosmologicalConstant Problem by dynamically sourcing the expansive Decoherence Tension (TD) required to maintaintopological compactness. The paper proposes a modified action principle, SCM, utilizing a stable, kineticscalar field Lagrangian LCco, successfully recovering the ΛCDM limit while predicting deviations (∆w ≈+0.05) during peak structural formation (z ≈ 2 − 3). This dynamical behavior is consistent with recentlyreleased Dark Energy Spectroscopic Instrument (DESI) data [7]. The observed extreme fine-tuning andnear-cancellation of contributions to the cosmological constant are interpreted as necessary consequences ofthe requirement that the manifold remain compact over cosmic history, implying a stringent 50/50 BalanceImperative on the relative strengths of compressive versus expansive interactions. The ultimate falsifiableprediction is the Sigma Trace—a persistent β1 loop detectable via Topological Data Analysis (TDA) in CMBpolarization maps.