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It is not the case that The finite-precision loophole (Meyer, Kent, Clifton 1999) shows that any KS-uncolourable set can be approximated by a colourable set within experimental error.
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Reasons For
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Reason for
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1.
The approximation requires context-dependent colourings that vary across measurement bases, undermining the core KS argument about non-contextuality.
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2.
Finite precision applies equally to both theory and measurement; allowing 'approximate colourability' arbitrarily weakens any impossibility proof.
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3.
KS targets logical consistency of value assignments, not measurement accuracy; approximation conflates distinct mathematical and empirical questions.
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Reasons Against
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Reason against
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1.
Experimental tests have finite precision; if KS sets differ from colourable sets only below measurement resolution, the distinction lacks empirical significance.
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2.
The loophole preserves realism by showing KS results don't require abandoning value-assignment; they require only acknowledging measurement limits.
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3.
Physics should distinguish between mathematical ideals and physical reality; KS uses infinite-precision constructs inaccessible to actual experiments.
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