Beyond the Continuum: Fractal Quantization as a Replacement for "R"

This paper presents a novel alternative to the classical real number continuum. Based on a cyclic and fractally quantized number space defined over the interval [0,11], the proposed model replaces uncountable cardinality with a countable, resonance-based structure. It eliminates the need for the Continuum Hypothesis and provides a coherent, information-preserving framework that may serve as a foundation for both mathematical and physical theories. The approach is fully deterministic, computable, and structured through prime-based difference sequences.

The work is conceptually connected to the author’s earlier work on number space quantization through prime-difference sequences

(“A New Perspective on Infinite Number Spaces through Prime Number Distances and Quantization” – DOI: 10.5281/zenodo.14853309),

but it stands as an independent framework focused on black hole topology and symmetry dynamics.