Research
Formal investigations in machine learning, quantitative modeling, and data-driven analysis, oriented toward reproducibility and tractable results.
Studies & analyses
Financial Distress Research
Distress prediction over roughly 105,000 firm-year observations, standardizing 60+ financial ratios. K-Means segmentation feeding cluster-aware logistic regression reached 81% accuracy and 0.84 ROC-AUC. XGBoost scored higher at 0.90. I kept the interpretable model: the target was regulatory early warning, where being able to explain a flag matters more than the score.
Student Engagement Analysis
Clustering and PCA applied to longitudinal student engagement records from ProofX infrastructure. Identifies behavioral cohorts and participation trajectory signals from institutional data. Documented as a technical report.
Computational Analysis of Collatz Dynamics
Early-stage computational research on Collatz total stopping time distributions across structured integer classes. Used large-scale simulations and visualization to compare prime and composite behavior, surface empirical regularities, and guide later ProofX architecture for deterministic integer-dynamics experiments.
Integer Explorations
Open questions and computational traces from ProofX runs. Nothing here is a proof.
Collatz Stopping Time Distribution
Distribution of stopping times across initial values up to 2^28. Measured trajectory length to 1 for each seed. Distribution exhibits a heavy tail with outlier clustering near powers of 2. No deterministic pattern in outlier placement identified.
Parity Transition Density
Computed odd-to-even transition ratios within Collatz trajectories across a stratified sample of initial values. Investigated whether parity alternation frequency correlates with stopping time. Preliminary analysis shows no consistent monotonic relationship.
Generalized 3n + k Extensions
Investigated Collatz-type variants using 3n + k for odd values of k. Examined cycle existence and divergence behavior across selected parameter values. Some variants exhibit verifiably periodic behavior under constrained domains; the general case remains open.