A sensible phenomenology of the complex phase diagram and rich phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this talk, I will identify a set of the most essential organization principles for the doped Mott insulator, which are argued to have captured the fundamental physics of the cuprate superconductor. Then I will exemplify their nature as the exotic long-range entanglement of many-body quantum mechanics by using the exact numerical tools of exact diagonalization and density matrix renormalization group, which are applied to some special cases of finite size/limited geometry to demonstrate the consequences of the general principle. Next, I will focus on the phase diagram relevant to the experiments in the cuprate, and show that it may be unified by a “parent”ground state ansatz constructed based on the organization principles. Here the superconducting state is of non-BCS nature with modified London equation and new elementary excitations. In particular, the two-gap structure and dichotomy between the nodal and antinodal regimes in the superconducting state, the origin of Fermi arc in the pseudogap regime, and the strange metal behavior in the high-temperature regime will be discussed as part of the emergent phenomenon.