A new high-resolution and genuinely multidimensional numerical method for solving conservation laws is being developed. It was designed to avoid the limitations of the traditional methods and was built from ground zero with extensive physics considerations. Nevertheless, its foundation is mathematically simple enough that one can build from it a coherent, robust, efficient, and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid change, such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting numerical solution should automatically be consistent with the properties derived from the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by avoiding the explicit use of the above derived properties. Specifically, to capture physics as fully as possible, the method requires that: (i) space and time be unified and treated as a single entity; (ii) both local and