In order to clarify the high-Tc mechanism in inhomogeneous cuprate layer superconductors, we deduce and find the correlation strength not revealed before, contributing to the formation of the Cooper pair and the 2-dimensional density of state, and demonstrate the pairing symmetry in the superconductors still controversial. To the open questions, the fitting and analysis of the diverging effective mass with decreasing doping, extracted from the acquired quantum-oscillation data in underdoped YaBa 2 Cu 3 O 6+x superconductors, can provide solutions. In this research, the results of the fitting using the extended Brinkman-Rice(BR) picture reveal the nodal constant Fermi energy with the maximum carrier density, a constant Coulomb correlation strength BR =U/U c >0.90, and a growing Fermi arc from the nodal Fermi point to the isotropic Fermi surface with an increasing x. The growing of the Fermi arc indicates that a superconducting gap develops with x from the node (underdoped) to the anti-node (optimally or over-doped). The large BR results from the dx2-y2-wave metal-insulator transition for the pseudogap phase in lightly doped superconductors, which can be direct evidence for high-Tc superconductivity. The quantum critical point is regarded as the nodal Fermi point satisfied with the Brinkman-Rice picture. The experimentally-measured mass diverging behavior is an average effect and the true effective mass is constant. As an application of the nodal constant carrier density, to find a superconducting node gap, the ARPES data and tunneling data are analyzed. The superconducting node gap is a precursor of s-wave symmetry in underdoped cuprates. Furthermore, the halfflux quantum, induced by the circulation of d-wave supercurrent and observed by the phase sensitive Josephson- junction experiments, is not shown due to 'anisotropic or asymmetric effect' appearing in superconductors with trapped flux. The absence of d-wave superconducting pairing symmetry is also revealed.