Are there any legitimate experiments/papers out there that have shown a violation of the Bell Inequalities in purely classical systems in which local realism couldn't sanely be called into question? I mean real-world objects - a deck of cards, a pair of gloves, etc. Things whose properties are constrained and correlated, yet completely intrinsic and knowable through simple observation, but which are then separated and independently measured, and the measurements are subequently compared to see if B.I. violations occurred.
There are a few papers on the Internet that claim to show this in one form or another, but I'm not really in a postiion to judge if they're legitimate, so I'd rather just hear from the experts on whether they know of any instances where violations have been truly shown in classical systems, or even genuine attempts to test this.
If this has been shown, or if it ever were to be shown, what would this mean? Would it just demote entanglement to little more than a statistical quirk? Or would it shake the foundation of our understanding of statistics and information theory?
I hope the last part isn't too philosophical, but what I'm anticipating is something along the lines of, "no we've never seen this, and we will never see it because it would defy the laws of math and lead to a universe-ending paradox if we did." Or, "yes we can observe this in classical systems but it doesn't say anything about quantum entanglement because ___".
Edit I'm not sure the intent behind my question was clear based on some of the comments and responses, so let me ask it slightly differently.
I'm not questioning the Bell theorem or that quantum entanglement cannot be explained through any local HV model. What I'm asking is: ignoring the possibility of signaling or superdeterminism, are there any experiments testing whether macro/classical systems can ever behave in a way that would also contradict "realism" such that one could find violations of the BI without any quantum influences?
Again my understanding going into this is that the answer is no, but it would be very interesting indeed if it were yes.
Edit 2 I found a paper online by William McHarris, an apparently deceased former Michigan State University physics professor, entitled "Chaos and the quantum: how nonlinear effects can explain certain quantum paradoxes", which appears to be more legitimate than others and hasn't been mentioned yet, though it doesn't seem to be a peer-reviewed journal paper.
He says at page 7, "classical nonlinear systems are known to exhibit correlations, ranging from the directions of particles in tornadoes to the distribution of energies in cosmic rays — and at times these can be great enough to overlap with quantum correlations." (emphasis mine).
Is there any merit to this? Or am I misinterpreting what he's saying?