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What is the status of the Born Rule in axiomatic QM?

While physicists have tried multiple times and failed to derive the Born Rule (for example: https://arxiv.org/pdf/quant-ph/0409144.pdf). I was wondering what axiomatic Quantum Mechanics had to say ...
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Can we pass to the limit in Poincaré-Jaynes-Bretthorst interpolation and deconvolution?

In Science and Hypothesis, chapter XI, The calculus of probabilities, Henri Poincaré deals informally with the fundamental problem of interpolation. He concludes (see http://ia600308.us.archive.org/21/...
Pascal Orosco's user avatar