The Implosion of the Outside: Coherence of Existence Based on the Principle of Radical Non-Omission

Technical Summary This work presents the formalization of the Delta-Root System and its evolution toward a modern gravitational framework. The system is defined by the articulation of two fundamental operators: the delta (Δ), representing structural difference, and the root, understood as a generative principle of fundamental length. The formulation is developed under the principle of radical non-omission, ensuring that no structural element can be removed without collapse of the system. Key components include: Fundamental length ((\ell_0)) as the ontological basis of measurement. Universal invariant ((u = 2)), establishing duality as the minimal condition of existence. Temporal power ((k)), defined as the radical exponent governing the emergence of new structural states. Radical closure, guaranteeing that iterative delta-root operations return to the initial structural condition. Gravitational integration, where gravity is identified as the generative root of length, linking temporal identity and spatial extension. The system is expressed through axioms, theorems, and corollaries, ensuring reproducibility and internal consistency. Ontological constraints are explicitly stated: existence begins at 1 (not 0), and multiplicity requires at least two differentiated entities. Connections with advanced mathematical structures (Lie algebras, Hilbert formalism) are highlighted, situating the system within a broader theoretical landscape. The result is a universal modular grammar for invariants, capable of describing physical, logical, and ontological systems in a unified algebraic framework.