The Ξ∞ Equation: A Recursive Identity Framework within Alpay Algebra

This document introduces and formalizes the Ξ∞ equation, a symbolic identity construct within the framework of Alpay Algebra. It models recursive identity compression by integrating emotional memory, temporal structure, and symbolic convergence dynamics. The equation and its supporting architecture enable rigorous modeling of recursive psychological states and symbolic self-awareness. The paper includes: • A worked real-life identity shift by the author • A formal depthness metric definition • Symbolic state transitions via λ-layer compression • Commentary on the Ξ∞ construct • A future application section for symbolic AI cognition • A comprehensive appendix of all symbols This work is part of a larger initiative to develop a mathematically grounded identity and recursion engine for cognitive systems, AI introspection modules, and symbolic logic modeling. Author: Faruk Alpay ORCID: 0009-0009-2207-6528

Keywords

Depthness Metric, Identity Shift, λ-layer Dynamics, Symbolic Systems, Cognitive Modeling, Ξ∞ Equation, ∞, Ξ, Alpay Algebra, Ξ∞, Emotional Compression, Recursive Identity, Recursive Symbolism

Impact byBIP!

	selected citations These citations are derived from selected sources. 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).	0
	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.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Found an issue? Give us feedback

0

Average

Green