Recursive nD Cascading Tensors: Granular Data Classification by Residuals and Analytical Addressing for O(1) Searches

Abstract

ABSTRACT —This research introduces an analytical framework of structural temporal asymmetry for the management of high-density multidimensional data, establishing a modular architecture that decouples construction complexity from retrieval latency. The architecture segments an initial heterogeneous data stream of cardinality N through a cascade of structural dimensionality (3D → 2D → 1D), dynamically mitigating memory fragmentation and zero-padding overhead. By implementing a dual indexing scheme that combines content based hash mappings with direct coordinate-based hexahedral sub-indexing, the system entirely avoids sequential matrix traversals. While the space generation and semantic filling phases scale linearly as O(N ) in the backend, the direct retrieval and inspection of data from specific metadata entities execute in deterministic constant time O(1) within the frontend RAM. This formal design establishes the theoretical foundations for structural scalability and immunity to data fragmentation by the physical limits of hardware constraints.Note: English translation of the Spanish version of https://zenodo.org/records/21592611