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We constructed a Hilbert space representation of a contextual Kolmogorovmodel. This representation is based on two fundamental observables -- in thestandard quantum model these are position and momentum observables. Thisrepresentation has all distinguishing features of the quantum model. Thus inspite all ``No-Go'' theorems (e.g., von Neumann, Kochen and Specker,..., Bell)we found the realist basis for quantum mechanics. Our representation is notstandard model with hidden variables. In particular, this is not a reduction ofquantum model to the classical one. Moreover, we see that such a reduction iseven in principle impossible. This impossibility is not a consequence of amathematical theorem but it follows from the physical structure of the model.By our model quantum states are very rough images of domains in the space offundamental parameters - PRESPACE. Those domains represent complexes ofphysical conditions. By our model both classical and quantum physics describeREDUCTION of PRESPACE-INFORMATION. Quantum mechanics is not complete. Inparticular, there are prespace contexts which can be represented only by a socalled hyperbolic quantum model. We predict violations of the Heisenberg'suncertainty principle and existence of dispersion free states.Comment: Plenary talk at Conference "Quantum Theory: Reconsideration of  Foundations-2", Vaxjo, 1-6 June, 200

Contextual approach to quantum mechanics and the theory of the fundamental prespace