The OPi-Quantum Framework: A Unified Analytic Approach for Multidimensional Data Extraction from Semantic Text via Prime Number Theory and Kernel-Weighted Transforms

We introduce and analyze the OPi-Quantum Framework, a unified methodology for extracting multidimensional data-specifically audio, geometric, and thermodynamic profiles-from semantic text.The framework is built upon the "Fundamental Mapping" of characters to Prime Numbers, processed via the OPi transform, an integral transform based on a logarithmic cosine kernel k(t) = ln | cos(πt/ ln t)| .We employ the discrete OPiZ transform to treat semantic sequences as kernelweighted Dirichlet series, establishing rigorous convergence bounds comparable to the Riemann zeta function .By analyzing the pole structure of the associated OPi transforms, we derive "Spectral Stability" metrics that map to the Source-Filter model for audio synthesis, proving that the pole structure controls the decay rates of exponential modes .Furthermore, we construct OPi-weighted scale zeta functions to determine the fractal (Hausdorff) dimension of the text for visual decoding .Finally, we incorporate an entropy-corrected variational framework to quantify the "thermodynamic energy" of semantic sequences, providing a rigorous analytic link between number theory, dynamical systems, and quantum eigenstates .