Dear Declan
The paper that I mentioned by Gill shows the possibility of obtaining an asymptotically exact cosine curve by removing data according to a formula. I have written, a few years ago, a visual basic program (mimicking Chantal Roth's original java pprogram) to obtain the cosine curve but it does remove a lot of data (about 25%, by my memory?).
I am quite suspicious that you have an asymmetry of Alice in favour of Bob with respect to missing data: should not there be symmetry? But I confess that I am unclear as to how that asymmetry arose in the missing data. There is also the issue of how experienced experimentalists can keep on overlooking, if that is what they are still doing, remaining sources of 'missing data' after taking such pains to exclude all possible sources?
So does nature actually give a cosine curve or does it really give a sawtooth curve which morphs into a cosine curve when there are missing data? If the latter, I do not know enough to see what damage that would do to QM. I am not sure if 'entanglement' can be excised from QM without harming the rest of QM?
There is also a third option (Joy Christian's option) which is that space is not as flat as it may seem. There are 1500 posts at
http://retractionwatch.com/2016/09/30/physicist-threatens-legal-action-after-journal-mysteriously-removed-study/
discussing this option. That website closed after exhausting the time available of the chair/referee rather than coming to an agreement. The maths there uses Clifford Algebra.
There is an interesting brief essay in this contest by Richard Conn Henry whose main point, as I interpret it, is that we do not yet have the correct topology of 4-space. Having the correct topology may be relevant to the third option above?
It is one thing to remove simulated data from a program after generating it in assumed 'normal' space, but the question arises if that data were removed illegitimately or whether that data never really could exist in a space of the correct topology.
My own essay in this contest suggests (page 7) that there should be no random outcomes for Alice and Bob: as everything seems pre-determined. That would imply hidden variables and hence enforce a sawtooth curve and be incompatible with QM assuming space is normal or flat or R3. But with a modified topology of space there is the possibility of rescuing the cosine curve, though I am not sure of the effect on QM as 'entanglement' would cease to exist. The final paragraph on page 8 of my essay implies that spin may be a vital component of emergent space. And I do not know what effect that quantum spin would have on the topology of space.
Best wishes
Austin