TMDD: Oscillators, Invariants, Boundaries.Part III: Theorem on Guaranteed Spontaneous Structuring

This work presents and proves a fundamental property of the Tensor Model of Discrete Dynam-ics (TMDD) the theorem on guaranteed spontaneous structurization. It asserts that ina system of interacting θ-cells, random uctuation-based restructuring in an amorphous environ-ment deterministically leads to the formation of stable structures within nite time. This is not aprobabilistic process but a direct consequence of the ontological principles of the model: bound-edness of informational volume, existence of internal "breathing" modes, and relational nature ofconnections. The concept of relational distance as a measure of structural closeness, which precedesmetric distance, is introduced. The existence of a critical nucleus size is proven, beyond which thegrowth of an ordered cluster becomes irreversible. It is shown how the problem of "remoteness"naturally arises from this mechanism and is solved through the formation of structural resonancesand channels of directed information transfer. The theorem resolves the problem of "ne-tuning"of initial conditions in the Universe, demonstrating that order is not a low-probability event butan inevitable consequence of the fundamental ontology of a discrete informational network.