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There are no such events; all experienced reality is mindmade and is therefore completely reasonable
That which is called mind, consciousness or intellect preceds all phenomena, mind is their ruler mind-made are they.
Three aggregates are conjoined with consciousness; perception, feeling and synthesis. Form is not conjoined with consciousness. Form is synthesized by synthesis as form.
Contact at any sense base is associated with contact at mind base.
Thus it is not surprising that one can use mathematics to understand perceived reality and it appears as if it is based on these same philosophical principles, because it is. Therefore reality is inherently reasonable.
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Buddha called them views. These are discussed in "Net of all views" sutta.
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A feature of Buddhism is Noble Silence -- i.e. not getting drawn into speculation (or "unwise attention").
I don't want to complain about the question, but the first paragraph is fiction (referencing the Matrix) and the second is like a "thought experiment" but I don't know what you're saying with it or if it's a metaphor for something -- it appears to invite speculation (maybe someone took it? maybe you misremembered?) -- or it's perhaps a paradox.
There are KΕans, used in some traditions of Buddhism, I don't know that's related to this question though.
One or two suttas mention the four great references -- and according to that I'd say that your question is not the kind of thing that the Buddha talked about -- to that extent "Buddhism" doesn't say anything about that topic.
At the risk of sounding too new-Age I might add that buddhism points out that put-together things are impermanent -- and so are thoughts, that there are different thought-moments. Given that your second paragraph is no more than a thought-experiment, there's nothing very remarkable about a thought (like "a key") existing in one moment and not existing in another.