A Dual-Layer Approach to the Collatz Conjecture: Classical Algebra and Functional Symmetry

This study explores the Collatz Conjecture through a dual-layer framework combining classical algebraic iteration and functional sequence symmetry. The model investigates convergence behavior using iterative reduction dynamics alongside symmetry-based stabilization concepts to analyze why Collatz sequences tend toward the absorbing state of 1.

Originality and AI-use statement:
This work is an original research output by Begüm Yıldırım. AI tools, if used, were limited to language refinement, grammar correction, formatting, translation assistance, and clarity improvement. The conceptual framework, research direction, interpretation, models, and conclusions belong to the author. External sources, datasets, or prior works are cited where applicable.