Volume IV concludes a unified four‑volume architecture describing how reality emerges from constraint, recursion, and relation. The substrate is presented as a primitive informational object with no geometry, no time, and no dynamical evolution. Geometry, phase, chirality, and topology arise as the four minimal constraint classes required for any coherent relational world to exist. The induced world is the projection of these constraints, and the observer is the local fixed point where global consistency becomes visible. This volume develops the logic of constraint closure, the induced‑world identity, the role of Protologic, and the structural necessity of the observer. It completes the system by showing that the world is not contingent but the unique configuration compatible with the substrate’s internal consistency. MathType StatementAll mathematical expressions in this document were created using MathType and are preserved as embedded MathType objects. The plain‑text source for each expression is maintained separately to ensure long‑term compatibility and accurate rendering across platforms and archival formats. Depository StatementThis work is part of a four‑volume scientific monograph deposited across Zenodo, Figshare, and OSF to ensure permanent, redundant, and openly accessible archival preservation.