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Preprint . 2025
License: CC BY NC
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY NC
Data sources: Datacite
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Phi Blueprints: An Algebraic Framework for Recursive Series

Authors: Way, Arien;

Phi Blueprints: An Algebraic Framework for Recursive Series

Abstract

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.

Keywords

fibonacci, phi ratio, phi

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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