Mathematical research at the intersection of number theory, algorithms, and computational analysis
Introduced a purely arithmetic framework extracting either π or 1 from floor and ceiling operations on perfect squares, reframing π as a dominant attractor within a hidden combinatorial dynamical system in the integers.
Key Findings:
• Developed discrete layer sequences U(n) and L(n)
with residual representations
• Proved ~75% of integers μ drive products toward π
(accurate to 6 decimals at n=10⁶)
• Extended analysis to μ values up to 70,000 with
systematic validation
Independently conducted research from 2022–2024 on a novel spatial probability model within regular 2D polytopes. Proposed a Periodic Cotangent Function to model the probability distribution of a 0-polytope relative to the centroid and boundary.
Highlights:
• Presented at Indian Mathematical Society
Conference
• Developed novel probability distribution models
• Received valuable feedback from mathematical
community
Established novel algebraic framework for transforming Pascal triangle rows into Fibonacci numbers through systematic coefficient selection where cᵢ ∈ {-1, 0, 1}.
Technical Achievements:
• Developed six complete enumeration strategies with
CUDA GPU acceleration
• Achieved exhaustive analysis up to 3²² (31.4
billion combinations)
• Designed polynomial-time greedy algorithm with
O(n) complexity
• Demonstrated perfect success rate across Fibonacci
numbers F₁ through F₁₀₀₀
Independent research analyzing Édouard Lucas's Pascal Triangle Method for calculating the exact nth Fibonacci number without recursion. Compared Lucas's combinatorial approach to classical methods in terms of computational complexity and performance efficiency.
Research Focus:
• Computational complexity analysis
• Performance efficiency comparison
• Feasibility in resource-constrained environments
Active contributor to the Online Encyclopedia of Integer Sequences (OEIS), a globally recognized mathematical database.
Contributions:
• Authored closed-form formula for OEIS A259569 (now
cited globally)
• Corrected mathematical inaccuracies in A130823
• Improved sequence integrity and documentation
• Active contributor on the OEIS Wiki
Proposed a novel power-ratio function modeling the transition from instability to asymptotic certainty with applications spanning multiple domains.
Applications:
• Algorithm analysis and complexity theory
• Numerical methods and convergence analysis
• Fractal mathematics
• Machine learning feature scaling
• Quantum state transitions
• Financial modeling and risk assessment