On the Completeness of Quantum Mechanics: Sources, Records and Probabilities

Can quantum mechanics be complete without being fundamental? Under stated source, detector, and statistical conditions, we reconstruct the quantum representation and Born probabilities and prove complete algebraic closure of the admitted quantum predictions without requiring a collapse postulate. We further show that many familiar quantum paradoxes arise from conflating coherent processes with retained records or probabilities with realized outcomes. We also ask whether mathematics as a whole, or the source architecture itself, emerges from a deeper structure.