Geometric Quantification of Spectral Entropy in Non-Associative Phase Spaces for the Optimization of Error-Correcting Codes in Planck-Scale Vacua

Mathematical Applications of Science Fiction We present a rigorous derivation of spectral entropy density within non-associative phase spaces characteristic of string theory backgrounds with non-vanishing R-flux. By constructing a twisted spectral triple ( (A_H, H, \slashed{D}_H) ) over a non-associative algebra of octonionic observables, we generalize the Minakshisundaram–Pleijel zeta function to quantify the information content of Planck-scale vacua. We demonstrate that the failure of the Jacobi identity in the phase space coordinates manifests as a cohomological obstruction to information loss, effectively encoding vacuum fluctuations into a non-local stabilizer code. The main result, the Theron–Void Isomorphism, establishes a duality between the spectral entropy of the bulk geometry and the code distance of a boundary quantum error-correcting code (QECC). We prove that for a vacuum state to remain stable against decoherence induced by spacetime foam, the phase space must satisfy a specific quantization condition related to the third Stiefel–Whitney class. This framework provides an analytic optimization method for holographic error-correcting codes in quantum gravity.