= Solution
For a <spin singlet state>, quantum spin measurements along unit vectors $\mathbf a,\mathbf b$ predict $E(\mathbf a,\mathbf b)=-\mathbf a\cdot\mathbf b$. Take $\mathbf a_0=\mathbf z$, $\mathbf a_1=\mathbf x$, $\mathbf b_0=(\mathbf z+\mathbf x)/\sqrt2$ and $\mathbf b_1=(\mathbf z-\mathbf x)/\sqrt2$. These give
$$
\boxed{|E_{00}+E_{01}+E_{10}-E_{11}|=2\sqrt2>2.}
$$
The violation therefore excludes the whole conjunction of the sufficient assumptions, for any model reproducing these correlations. It does not identify which premise fails without further commitments about causal explanation, state completeness and measurement setting generation.
A defensible verdict is to retain ordinary independent setting preparation and reject <Bell local causality>, specifically its classical screening-off factorization. In standard <quantum theory>, taking the pure entangled state as the complete state preserves <parameter independence>: each local marginal is $1/2$, regardless of the distant setting. Yet <outcome independence> fails. For equal spin axes, $P(A=+,B=-)=1/2$, whereas $P(A=+)P(B=-)=1/4$. The distant outcome changes the conditional prediction even after the <quantum state> is specified. This failure is compatible with <quantum no-signalling>, since conditioning on that outcome requires learning a result which cannot itself be controlled.
Adding further past variables does not restore the entire Bell conjunction while retaining the violating correlations; the <CHSH inequality> already allowed arbitrary such $\lambda$. Alternatively, one may reject <measurement independence>, permit retrocausal setting dependence in the relevant past state, or adopt another non-Bell-local description. Those are logically possible responses, but each must explain its replacement probability and causal model rather than treating the inequality as a failed algebraic theorem. A deterministic theory is not exempt from this requirement.
The assumption of <measurement independence> is supported by the purpose and design of independently varied settings, but cannot be proved for every conceivable hidden variable merely by inspecting observed setting frequencies. Conversely, a rejection of <Bell factorization> does not alone establish a controllable superluminal signal or select a unique ontology. \b[The reasoned verdict is against Bell's screening-off locality, conditional on the other stated premises; the unconditional conclusion concerns their conjunction.]
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