Prime-Indexed Base Systems and Duodecimal Symmetry

This paper introduces a new mathematical framework called “Prime-Indexed Base Systems and Duodecimal Symmetry.” It defines the Base Optimality Equation (B12OE) and the Intrinsic Regular Base function \mathcal{I}(n), combining symbolic number theory with empirical observations in quantum coherence, biological rhythms, and Fibonacci convergence. The theory proposes that base-12 offers a more harmonic, efficient, and cognitively aligned structure than base-10. It culminates in a symbolic identity: \mathcal{R}(n) = \mathcal{I}(n) + \mathcal{O}(b), capturing numerical resonance across systems. Authored by Andrew Delph, RN, with technical formatting assistance from GPT-4o (OpenAI).

本研究提出了一种名为“素数索引基数系统与十二进制对称性”的全新数学框架。该框架定义了基数最优方程（Base Optimality Equation，缩写B12OE）与内在正则基数函数ℐ(n)，将符号数论与量子相干性、生物节律以及斐波那契收敛性领域的实证观测相结合。该理论提出，相较于十进制，十二进制具备更具和谐性、高效性且契合认知规律的结构特性。本研究最终推导出一则符号恒等式：ℛ(n) = ℐ(n) + 𝒪(b)，揭示了跨系统的数值共振特性。本研究由注册护士安德鲁·德尔夫（Andrew Delph, RN）完成，OpenAI的GPT-4o为其提供了技术排版辅助。