Alper Pektaş

Resolving Galactic Rotation Curves, Spacecraft Anomalies, and Solar Corona Heating

This paper addresses three major astrophysical paradoxes—flat galactic rotation curves, the Pioneer spacecraft decelerative anomaly, and the solar corona heating problem—by utilizing the deterministic $n^3$ matrix-mechanical framework. By rejecting unobserved constructs such as d...

Discrete Threshold Dynamics and $P_{shock}$ Dissipation

Traditional ethology and fluid dynamics frequently treat biological responses and high-velocity aerodynamic stress through continuous, smoothed approximations. Within the deterministic $n^3$ matrix-mechanical framework, biological systems serve as empirical exemplars of discrete...

Mechanical Dynamics: Emergent Mass, Frequency Translation, and Orbital Mechanics

Traditional continuous field theories and point-mass gravitational models often struggle to unify high-energy core dynamics with stable, non-collapsing macroscopic structures. In this paper, we propose a novel ``Mechanical Dynamics'' framework where fundamental constants of class...

Corvid Acoustic Calibration, Fibonacci Equilibrium, and the Under-Saturated Space Matrix

Traditional ethology often treats biological responses to environmental shifts through abstract or anthropomorphic assumptions. Within the $n^3$ matrix-mechanical framework, however, the morning rhythmic vocalizations of corvids are reinterpreted as autonomous environmental energ...

Mechanical Dynamics

This monograph establishes a rigorous mechanical framework that reinterprets classical dynamics, relativistic phenomena, and cosmological anomalies through first-principles particle matrix interactions. By substituting abstract geometric curvatures and unobserved entities with co...

Mechanical Dynamics

This monograph establishes a rigorous mechanical framework that reinterprets classical dynamics, relativistic phenomena, and cosmological anomalies through first-principles particle matrix interactions. By substituting abstract geometric curvatures and unobserved entities with co...

Mechanical Dynamics

This monograph establishes a rigorous mechanical framework that reinterprets classical dynamics, relativistic phenomena, and cosmological anomalies through first-principles particle matrix interactions. By substituting abstract geometric curvatures and unobserved entities with co...

Formalization of the ${Ddpr}{(Dupertation})$ Operator

Classical combinatorics employs the permutation operator $P(n, r)$ to measure ordered selections by treating elements as abstract, invariant multipliers. This approach neglects the physical state transitions of the background depository ($n-r$). We propose the \textbf{$\mathrm{Dd...

The Added Groups in the Collatz System

This note demonstrates that the step count in the Collatz process cannot be infinite. Furthermore, the implications of the existence of a single external orbit are discussed, aiming to prove that such an orbit does not exist.

Bit-Level Finiteness, Pre-Root Architecture and Framework for Collatz Trajectories

This paper establishes a rigorous bit-level and modular framework for resolving the Collatz conjecture. By bypassing intermediate even division steps via a generalized shortcut operator, we prove that infinite climbing ($k=1$ states) leads to a structural finiteness contradiction...

Formalization of the ${Ddpr}{(Dupertation})$ Operator

Classical combinatorics employs the permutation operator $P(n, r)$ to measure ordered selections by treating elements as abstract, invariant multipliers. This approach neglects the physical state transitions of the background depository ($n-r$). We propose the \textbf{$\mathrm{Dd...

Formalization of the ${Ddpr}{(Dupertation})$ Operator

Classical combinatorics employs the permutation operator $P(n, r)$ to measure ordered selections by treating elements as abstract, invariant multipliers. This approach neglects the physical state transitions of the background depository ($n-r$). Under the $\mathrm{Ddpr}$ framewor...

Formalization of the ${Ddpr}{(Dupertation})$ Operator

Classical combinatorics employs the permutation operator $P(n, r)$ to measure ordered selections by treating elements as abstract, invariant multipliers. This approach neglects the physical state transitions of the background depository ($n-r$). Under the $\mathrm{Ddpr}$ framewor...

Water ($H_2O$) $Molecule Geometry$ and the $\frac{\pi}{2}$ Equilibrium

This paper presents the exact, error-free mathematical formulation of the intramolecular angular equilibrium for the water molecule ($H_2O$), establishing a framework where the structural ratios perfectly converge to the mathematical constant $\frac{\pi}{2}$. By accounting for sc...

Cycle Elimination in Collatz Trajectories via Cross-Constraint System Reduction

In this study, trajectory behaviors of odd numbers in the Collatz process are analyzed through the intrinsic operator dependency between k odd steps and n even steps (n = f · k). We introduce the method of Cross-Constraint System Reduction, which bridges forward and reverse traje...

Layered Grouping of Numbers According to Step Depth in Collatz Dynamics

In this study, a systematic classification of odd integers in Collatz trajectories according to their step depths and modular layers is presented. Odd numbers are categorized into n-th Groups and ROOT Groups based on the step count required to reach a known node value after the i...

Layered Grouping of Numbers According to Step Depth in Collatz Dynamics

In this study, a systematic classification of odd integers in Collatz trajectories according to their step depths and modular layers is presented. Odd numbers are categorized into n-th Groups and ROOT Groups based on the step count required to reach a known node value after the i...

Branchless O(1) Shortcut Architecture for Collatz Simulations

This study introduces a high-performance, branchless computing framework designed to eliminate conditional logic bottlenecks and intermediate parity checks in Collatz trajectory simulations. By decomposing the 3n+1 operator into modular G1/G2 parity components, we derive a genera...

Branchless O(1) Shortcut Architecture for Collatz Simulations

This study introduces a high-performance, branchless computing framework designed to eliminate conditional logic bottlenecks and intermediate parity checks in Collatz trajectory simulations. By decomposing the 3n+1 operator into modular G1/G2 parity components, we derive a genera...

General 2^{k}-Division Shortcut Operator and Modular G_{1}/G_{2} Decomposition for Hardware-Level O(1) Throughput Enhancement in Supercomputers for the Collatz Problem

In this study, a general algebraic shortcut operator is derived to eliminate iterative steps and intermediate parity checks in Collatz (3n+1) trajectory simulations. By integrating G_{1}/G_{2} modulo 8 classification, the framework achieves 100% coverage over all positive odd int...