  The fabled violation of Bell's inequality by the probabilistic specifications
of quantum mechanics is shown to derive from a mathematical error. The
inequality, designed to assess consequences of Einstein's principle of local
realism, pertains to four polarization products on the same pair of photons
arising in a gedankenexperiment. The summands of the CHSH quantity $s(\lambda)$
inhere four symmetric functional relations which have long been neglected in
analytic considerations. Its expectation $E[s(\lambda)]$ is not the sum of four
``marginal'' expectations from a joint distribution, as quantum theory
explicitly avoids such a specification. Rather, $E[s(\lambda)]$ has four
distinct representations as the sum of three expectations of polarization
products plus the expectation of a fourth which is restricted to equal a
function value determined by the other three. Analysis using Bruno de Finetti's
fundamental theorem of prevision (FTP) yields only a bound for $E(s)$ within
$(1.1213, 2]$, surely not $2\sqrt{2}$ at all. The 4-D polytope of cohering
joint $P_{++}$ probabilities at the four stipulated angle settings are
displayed as passing through 3-D space. Aspect's ``estimation'' is based on
polarization products from different photon pairs that do not have embedded
within them the inhering functional relations. When you do actively embed the
restrictions into Aspect's estimation procedure, it yields an estimate of
1.7667, although this is not and cannot be definitive.
