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. Acknowlegdement:I would like to acknowledge my Lenovo laptop, which very nearly met its maker during a BIOS update the night before this submission. For thirty‑five long minutes it lay motionless, fans silent, screen dark, giving every impression that its spirit had departed. I had already begun preparing the metaphorical casket, rehearsing the eulogy, and lighting the incense for its final journey. But then — in a moment worthy of a WWE pay‑per‑view — the machine jolted back to life like The Undertaker rising from the mat. No warning, no explanation, just a sudden resurrection and a return to full operational strength. This document was completed on that very laptop, whose improbable comeback deserves formal recognition. I would also like to acknowledge The Undertaker — a figure who has been a constant presence from my earliest memories of watching WWF at three years old, right through to today as I watch him speak openly about his life, career, and discipline. His legacy has always been more than wrestling: a symbol of endurance, presence, and absolute commitment to the craft. Across every era, every storyline, and every universe you could imagine, he remains a legend in the purest sense of the word. The energy of his iconic “rise from the mat” moment feels like it echoed directly into my laptop’s own unexpected resurrection, and it deserves recognition here. -matt Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com
Matthew Arthur Carlo (Sun,) studied this question.