March 3, 2026Open Access

Admissibility Framework I - Constitution and Readout

Key Points

The study reveals that bounded transitions in arithmetic dynamics are determined by internal structural conditions.
Importantly, the frame constant CCC defines limits on maximum admissible transition distances without relying on probabilistic criteria.
A deterministic state-selection process reformulates prime selection based on allowed transitions within a specific configuration space.
The findings emphasize that controlled arithmetic readout is achievable when the underlying state space is structurally closed.

Abstract

This paper studies a concrete readout mechanism arising from a structurally constrained arithmetic dynamics on the integers.Building on a prior framework in which admissible arithmetic transitions are determined by intrinsic structural conditions rather than probabilistic or heuristic criteria, we introduce and analyze a frame constant CCC, which bounds the maximal admissible transition distance in the associated resonance space. The constant CCC is not an externally imposed cutoff, nor a statistical property of prime gaps.Instead, it emerges internally from the cumulative growth of a resonance barrier defined by a single observable on a fixed logarithmic–phase frame.Transitions exceeding CCC are shown to be structurally non-existent rather than merely suppressed or unlikely.This induces a light-cone–like admissibility structure on arithmetic evolution, in which forward transitions are permitted only within a bounded cone determined by the frame. Within this setting, prime selection is reformulated as a deterministic state-selection process over an admissible configuration space.No probabilistic model, machine learning component, or randomness assumption is used.The resulting readout is shown to be stable under changes of initial data, sampling resolution, and internal optimization paths, while remaining sensitive only to frame-level parameters. The purpose of this paper is not to claim an ultimate predictive algorithm, but to demonstrate that controlled arithmetic readout becomes possible once the underlying state space is structurally closed.Possible computational realizations are discussed only as secondary consequences of this structural fact. AI Usage Declaration: The core concepts and mathematical intuitions of this paper were conceived by the author (Byeong-Young Oh). The technical formalization of the mathematical framework and the English drafting process were performed in collaboration with Artificial Intelligence (AI) models. The author takes full responsibility for the contents and logical integrity of this work. This work is part of an ongoing independent research program. Official research index :https://jingyu-papa.github.io/publications/

Admissibility Framework I - Constitution and Readout

Key Points

Abstract

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