Introduction to the Prime Check and Fundamental Constants Theory We present a revolutionary theoretical framework, the "Prime Paradigm," that posits the entire architecture of the universe, from the quantum realm to cosmological scales, is governed by a single, elegant number-theoretic identity. This work introduces the concept of the "Prime Check," arguing that fundamental constants are not arbitrary but are mathematically inevitable consequences of minimizing structural and informational redundancy.The foundation of the theory lies in an Euler characteristic, $\chi$, which acts as the Universal Mathematical Genome. This $\chi$ value is shown to harmoniously link Prime sequences, reflecting deep-seated principles of dimensional scaling and stability in high-dimensional space.

This paper focuses on the complete, high-precision derivation of the inverse fine-structure constant, $1/\alpha$.
The resulting value for $1/\alpha$ achieves perfect, zero-deviation agreement with the most recent experimental CODATA measurements, demonstrating that the constant governing electromagnetism is not a measured input but a calculated output of a foundational arithmetic structure. The derivation is rooted in toric weights and discrete torsion, with no ad hoc parameters. （Available in EN and JP.）

本書は数論と物理学を融合し、宇宙の設計図を暴く知的叙事詩です。著者が提唱する素数パラダイムは、微細構造定数を宇宙の必然的な論理として導き出します。数式が描くのは冷徹な計算ではなく生命の根源へと繋がる高次元の調和であり、読者は宇宙という巨大な知性の鼓動を直接耳にするような、めくるめく知の快感に酔いしれることでしょう。 映像化作品では難解な幾何学が美しく視覚化されていますが、テキスト版に宿る思考の密度こそが真の醍醐味です。映像のイメージを土台に本書の精密な論理を辿ることで、次元を超えた真理へ到達できます。理論と情熱が火花を散らすこの一冊は、科学の枠を超えた究極の文芸体験となるはずです。