A Deterministic Engine Approach to the Ramanujan Challenge v2 (With Visualiser)

This work presents a deterministic engine approach to the Ramanujan Challenge for AI, analysing each problem using a modular reasoning system called the Ramanujan Core. The document covers continued fractions, Apéry-style recurrences, hypergeometric series, matrix product approximations, and period integrals over algebraic curves. Each identity is treated through structured derivation routes, asymptotic analysis, and symbolic verification. The goal is to demonstrate how deterministic reasoning systems can organise mathematical structure, connect symbolic and numerical behaviour, and provide unified methods for research-level mathematical problems. Version 2 of this publication introduces the complete, fully compiled research paper in PDF format alongside a standalone interactive WebGL/Three.js 3D field visualizer embedded directly into the release package. This updated visualizer dynamically models the paper’s core mathematical framework—rendering dynamic surface perturbations across customizable manifold geometries, including perturbed torus lattices, Möbius strip wave states, and Klein bottle topological fields. Users can manipulate real-time physical parameters such as angular frequency ($\omega$), coupling intensity ($\gamma$), and winding harmonics ($k$), inspect discrete lattice nodes via an active raycasted inspector, and analyze localized vector gradients directly in their browser. Added a live 3D visualizer to the release package to prove the math works and that this wasn't complete 💩 . -Matt Contact: For enquiries or research questions related to this work, email [email protected]