Arithmetic Loophole in Bell's Theorem: Overlooked Threat to Entangled-State Quantum Cryptography

Bell's theorem is supposed to exclude all local hidden-variable models of quantum correlations. However, an explicit counterexample shows that a new class realistic models, based on generalized arithmetic and calculus, can exactly reconstruct rotationally symmetric probabilities typical two-electron singlet states. Observable are consistent with the usual employed by macroscopic observers, but counterfactual aspects sensitive choice calculus. The model classical in sense Einstein, Podolsky, Rosen, Bell: elements reality exist modeled integrals probaility densities. Probability densities have Clauser-Horne product form theories. neither nor integral representation rotations ones. has standard properties only respect defines product. Certain formal transformations expressions one finds proofs \`a la Bell do not work, so Bell-type inequalities cannot be proved. system we consider deterministic, local-realistic, invariant, observers free will, detectors perfect, canonical loopholes discussed literature.