The Infinite Cabinet: A Non-Parametric Framework for Data Analysis through Intrinsic Addressing

This article presents the Infinite Cabinet, a non-parametric framework for the analysis of data and enumerable sets, in which each data value simultaneously constitutes its own structural address. The method introduces a discrete, level-based access architecture, taking zero as the structural reference, such that positive values occupy positions in the positive domain and negative values occupy mirrored positions in the negative domain. From the ordering of the set and the traversal of these addresses, an intrinsic curve emerges, generated exclusively by the data themselves, without the prior imposition of a model function (exponential, logarithmic, polynomial, etc.). Unlike traditional modeling approaches, the Infinite Cabinet explicitly separates two stages: (i) the non-parametric structural extraction of the set’s curve and (ii) optional parametric modeling, performed only a posteriori, if desired. As case studies, the framework is applied to the prime numbers, recovering their known characteristic curve through asymptotic approximation, and to a set of machine failure times during a work shift (minutes 6, 10, 25, 140, 280…), showing how the cabinet produces an intrinsic curve and how a functional model may subsequently be extracted for analysis and prediction purposes. The method is general and applicable to data in mathematics, physics, engineering, and data science.