Alper Pektaş

Why Scale-Invariant Modular Shortcuts Extend to Infinity: Asymptotic Natural Density and Ergodic Limits under 10^k Partitioning

This paper formally demonstrates why the scale-invariant shortcut architecture developed for the Collatz conjecture rigorously extends from finite computational bounds (10^{10000}) to the infinite limit (N \to \infty). By evaluating the bounded interval I_k = [1, 10^k], we establ...

From Micro-Details to Global Closure: A Unified Framework for Collatz Trajectories via Two-Group Modular Partitioning

Moving from local micro-structural details to global analytical closure, this paper establishes a comprehensive framework for Collatz (3n+1) trajectory analysis. By bridging foundational two-group modular partitioning (G_1 and G_2 modulo 8 classes) with non-iterative meta-optimiz...

Reduction of the Numbers in the Collatz Equation into Two Groups and the Results

This study presents a framework for classifying Collatz trajectories by separating their step relations into two fundamental iterative groups. The groups are constructed directly from numerical relations observed between the successive values of Collatz trajectories. Each group h...

Reduction of the Numbers in the Collatz Equation into Two Groups and the Results

This study presents a framework for classifying Collatz trajectories by separating their step relations into two fundamental iterative groups. The groups are constructed directly from numerical relations observed between the successive values of Collatz trajectories. Each group h...

Scale Invariance and Dynamic Invariants in Collatz Dynamics

In this study, the fundamental components of numbers, their periodic scaling in positional numeral systems, and their cyclical behaviors are investigated within an academic framework. It is demonstrated that every element in the set of numbers is a derivative of base combinations...

Linear Approximations in Exponential Functions and the Deconstruction of Permutational Redundancies: A Dynamic Person-Capacity Model

This paper establishes the definitive mathematical formulation of the "Person-Capacity-Preference" model, originally conceptualized by Alper Pektas. While linear approximations fail to model the curved trajectories of exponential fields, this framework introduces a Dynamic Correc...

Linear Approximations in Exponential Functions and the Deconstruction of Permutational Redundancies: A Dynamic Person-Capacity Model

This paper establishes the definitive mathematical formulation of the "Person-Capacity-Preference" model, originally conceptualized by Alper Pektas. While linear approximations fail to model the curved trajectories of exponential fields, this framework introduces a Dynamic Correc...

Linear Approximations in Exponential Functions and the Deconstruction of Permutational Redundancies: A Dynamic Person-Capacity Model

This paper establishes the definitive mathematical formulation of the "Person-Capacity-Preference" model, originally conceptualized by Alper Pektas. While linear approximations fail to model the curved trajectories of exponential fields, this framework introduces a Dynamic Correc...