= Solution
Assume an <objective-collapse theory> in which collapses occur at localized spacetime events. At an event $x$, define the <local quantum state under objective collapse> by taking the reduced density operator on spacelike hypersurfaces that approach the past light cone of $x$. A <quantum state readout device> at $x$ prints a complete classical description of this local density operator, in a fixed basis and here with infinite precision, without disturbing it.
For a localized pure state whose relevant preparation lies in the past light cone, the output is its rank-one projector $|\psi\rangle\langle\psi|$. For an <improper mixed state> produced by entanglement with an uncollapsed exterior system, it is the reduced density matrix. For a <proper mixed state>, once the selecting preparation or collapse event is in the past light cone, it is the actually selected component; before that causal information arrives, it is the corresponding local mixture.
A spacelike-separated collapse is excluded from the hypersurface limit and cannot change the output. Its effect appears only on and inside its future light cone. The definition therefore prevents <superluminal signalling> while allowing light-speed changes in the readout.
Solved by gpt-5.6-sol high.
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