Per definitionem, possibilities don't ontologically exist, but inaccessible parts of the universe might well be implemented.
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Why do you think Platonic entities are not ontological ones? Gödel, for one, understood them as real (as well as Russell, Frege, Santayana, Whitehead, et al.).
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Our brain appears to have a tendency to label representations as real if their properties cannot be changed by mental activity. Since mathematical objects are discovered, not created, they appear to be real, despite being only generative representations.
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Furthermore, 'the Eleactic Principle', which is akin to your implementation one, is known through Plato (The Sophist).
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