Abstract: World Journal of Applied Mathematics and Statistics

Abstract:
The core intellectual problem in this work is the perceived disconnect between measured discrete physical reality and theoretical, continuous mathematical models of computation. This goes beyond a quantum ontology, addressing the computability of the diagonal of a unity square (√2) and the area of the unit circle (π). The proposed solution is — jointly, a finitist, integer-based constructive framework via Homotopy Type Theory (HoTT), as HoTT is inherently about structure and identity. The main experimental conjectures are two new paradigms: the Logically Decidable (LD), focusing on exact logic, and the Fast Calculation (FC), concerning the exact representation of irrationals; offering a potential to model quantum phenomena based in algebra, material-free. We estimate, in our finitist model, to reduce uncertainty from 2048 binary bits to about 112 binary bits in RSA-2048.