Modulational Interaction Between Multiverses: Mechanism, Formalization, and Fold Restructuring

The article formalizes the mechanism of interaction between multiverses within the Hierarchical Pulsating System of Realities (HPSR). In previous works of the series, the term "tidal forces" was used for this mechanism as a metaphor. In the present work it is abandoned, and a more accurate term is introduced — "modulational interaction." Classical tidal forces act on massive objects through the gradient of a gravitational field. In HPSR the interaction acts not on objects but on equilibrium parameters, and changes the structure of folds. Folds are not objects but stable configurations of space-time. Therefore the classical model does not fit. Modulational interaction is defined as the modulation of the equilibrium parameters of one multiverse under the influence of another. It depends on the distance d, the "mass" of the multiverses, and relative velocity of motion. The mechanism is illustrated by the Eiffel Tower metaphor: R does not attract the steel beams but changes the properties of the steel — melting point, capacity for oxidation. Similarly, R modulates the equilibrium parameters of R₀ locally and differentially, which leads to the restructuring of folds. Properties of modulation: locality, differentiation, irreversibility. A mathematical sketch is given: V(A) → V(A) + δV(A, d, R); A → A' = A + δA, where δA is determined from the condition of minimum of the new potential. A comparison with classical tidal forces is conducted along five aspects: what acts, what changes, mechanism, speed of transmission, reversibility. Verifiable consequences are discussed: CMB anomalies, H0 tension (5σ), distribution of galaxies, variations of constants. Open questions are formulated: the nature of the interaction, dependence on distance, speed of transmission, the need for renaming throughout the MBM series. Without modulational interaction HPSR is static; with it — dynamic and verifiable.