Phi Blueprints: An Algebraic Framework for Recursive Series

This paper introduces the concept of Phi Blueprints—fundamental numeric constants that offer an alternative algebraic framework for deriving values within all nine Phi Series. Traditionally, each term in a Phi Series arises from the sum of its two predecessors. However, through pattern analysis, a set of constants—72, 137, and 161—emerged, which, when combined in specific proportions, yield any value within the series using simple equations. These constants are formalized as the Omega Blueprint (ΩB), the Alpha Blueprint (αB), and the Phi Blueprint (фB), each representing distinctive numeric signatures. The notion of Phi Blueprints was not initially theorized but was revealed through broader pattern analysis, suggesting an underlying structure to the Phi Series that is algebraically expressible. This exploration lays the groundwork for future study into these constants and their implications for mathematical pattern recognition and series generation.