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The UOF Hypothesis: Uncomputable Order Fractality and the Algorithmic Dimension of Permuted Partial Sums
2026-09-04
We formulate a new hypothesis at the intersection of fractal geometry, the theory of divergent series, and algorithmic information theory. The hypothesis asserts the existence of a computable sequence whose partial-sum graph is fractal, whose Hausdorff dimension changes under permutation of its terms, and for which the resulting dimension function is algorithmically non-computable. Unlike previous formulations, we provide a constructive ansatz for such a sequence based on rapidly growing phases encoding the halting set. We give a fully detailed mathematical formulation, discuss its components, and connect the hypothesis to existing results and to several recent works of the author. The present work also includes an extensive discussion of possible proof strategies and the main technical obstacles that must be overcome. Two complementary approaches are developed: a topological-existential strategy yielding a weakened form, and an analytic-constructive strategy that, conditional on a new dimensional growth lemma, would establish the hypothesis in full generality.
Ссылка для цитирования:
Тишков В. В. 2026. The UOF Hypothesis: Uncomputable Order Fractality and the Algorithmic Dimension of Permuted Partial Sums. PREPRINTS.RU. https://doi.org/10.24108/preprints-3116301
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