Contemporary scientific methods and ways to explore the world are based on its deep and detailed quantitative analysis using diverse numerical methods. However, there is no numerical method that could be used to assess qualitative properties of objects. Studying of systems' qualitative states is purely descriptive on a "post-factum" basis. In this work it is shown that there are objective laws unknown to date, the knowledge of which completely removes all obstacles on the way to formulation of philosophically and scientifically grounded numerical method of qualitative analysis of the Universe. As a result of the conducted research, the theory of quantity-to-quality transitions was developed, which lets us track any changes of qualitative state of a system (or an object) in detail. Thereby an analytical way to solve a huge variety of problems of qualitative nature is formulated, which meets the criteria of internal consistency, isolation, compactibility and mathematical simplicity. Thus, the scientific from of cognition of the world gains completeness regarding research methods, which can henceforth systematically make use of numerical methods of both quantitative and qualitative analysis.

          Discovery of the law of bipolarity allows us to explain such immanent properties of the matter as its duality and tripletness. An analytical method is presented, which can be used to determine numerical measure of a system's transfer from one qualitative state to another when its quantitative parameters change.

          Using the developed numerical method of qualitative analysis, an option for adjusting chaotic inflationary cosmology is found, the theoretical limit of the absolute zero is determined, a restriction on the qualitative diversity of the string landscape is introduced and a hypothetical neutral particle having a common origin with an electron and a positron is predicted.

          An assumption is made about a new form of existence of matter - energine form, which structures the cosmological vacuum.

          The hypothesis is substantiated that it is necessary to appropriately adjust the Planck constant based on the law of bipolarity when building multidimensional models of the Universe. A possibility of dynamic lowering of the spatial metric of the world as a non-integer value is given.

          The results of this work allow the scientific form of cognition of the world to gain completeness regarding research methods, which is expressed in the accord of numerical methods of quantitative and qualitative analysis.

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