The single-slit and double-slit experiments are among the most fundamental demonstrations of quantum behavior. Every interpretation of quantum mechanics must account for them, yet none has derived the mathematical structures used todescribe them from the experiments themselves. In this paper we show that Fractal Uncertainty Theory (FUT) achieves precisely this. The which-way measurement problem is resolved without wave-function collapse or many worlds.We argue that the slit experiments, properly understood through FUT, constitute the physical origin of arithmetic itself. Note on status. This document represents the current state of FUT development as of February 2026.Predictions may be refined or extended as the theoretical framework develops and experimental capabilities advance.
This work is Part II of a two-part series on the Modular Superselection Framework. Part I (DOI: 10.5281/zenodo.17834017) established the theoretical foundation; Part II provides computational validation through AlexMax-Q discrete quantum dynamics. Building upon the Modular Superselection Framework established in Part I (Lazzari, 2025; DOI: 10.5281/zenodo.17834017), we present a concrete computational implementation showing that discrete ℤ_M-graded state spaces can support robust quantum interference. Using AlexMax fractal-arithmetic encoding to construct natural-number states organised into modular sectors, we systematically explore the emergence of quantum behaviour in a fully discrete setting. We identify a sharp distinction between purely geometric models and dynamically driven ones. In Framework v1.x, where overlap is determined solely by a fractal metric and discrete phase assignments, the resulting quantum–classical deviations never exceed ≈3%, placing the model firmly in a quasi-classical regime. In Framework v2.0, by contrast, we introduce explicit unitary dynamics generated by fractal-weighted Hamiltonians. Numerical simulations reveal strong interference, with quantum–classical deviations ranging from 18% to 43% across a broad parameter range of fractal decay rates, path asymmetries, and coupling geometries (fractal, modular, hybrid). These results provide the first explicit computational realisation of the postulates formulated in Part I: modular-arithmetic structures, when equipped with sector-preserving unitary evolution, can generate genuinely non-classical correlation patterns while maintaining a deterministic, ℤ_M-graded description of measurement. The AlexMax-Q framework thus connects number-theoretic fractal geometry with discrete quantum dynamics and supports an epistemic interpretation of quantum measurement within ℤ_M-graded structures.
A closer examination of Eberly ``revivals,'' Berry ``quantum fractals,'' and Schleich ``carpets'' exposes a simple unitary-cyclic group structure in the dynamics of wave packets for rotorlike systems with quadratic spectra. Quantum quasifractal patterns are revealed to be permeated by self-similar ``X-braid'' structures seen by Hofstadter in Zeeman-perturbed band structures and in other spectra related to circle maps. The patterns are shown to correspond to revival dynamics in the flow of energy or information through these N-level systems with X-braids being directly related to quantum beats or elementary U(2) resonance transfer.
CN-group analysis and Farey arithmetic discretely catalog X-braid hierarchy and suggest the possibility of homocyclic nanostructures or
CN circuits that are base-N digital quantum computing registers. The phase dynamics corresponds to a fairly sophisticated integer arithmetic that includes an output of all rational numbers resolvable by a given energy input.
CN circuits automatically give all factors of N. The dynamics of a
C6 device is discussed in detail.