This manuscript presents a study with recruited volunteers that comprehends three sorts of events present in Alzheimer's Disease (AD) evolution (structural, biochemical, and cognitive) to propose an update in neurodegeneration biomarkers for AD. The novel variables, K, I, and S, suggested based on physics properties and empirical evidence, are defined by power-law relations between cortical thickness, exposed and total area, and natural descriptors of brain morphology. Our central hypothesis is that variable K, almost constant in healthy human subjects, is a better discriminator of a diseased brain than the current morphological biomarker, Cortical Thickness, due to its aggregated information. We extracted morphological features from 3T MRI T1w images of 123 elderly subjects: 77 Healthy Cognitive Unimpaired Controls (CTL), 33 Mild Cognitive Impairment (MCI) patients, and 13 Alzheimer's Disease (AD) patients. Moreover, Cerebrospinal Fluid (CSF) biomarkers and clinical data scores were correlated with K, intending to characterize health and disease in the cortex with morphological criteria and cognitive-behavioral profiles. K distinguishes Alzheimer's Disease, Mild Cognitive Impairment, and Healthy Cognitive Unimpaired Controls globally and locally with reasonable accuracy (CTL-AD, 0.82; CTL-MCI, 0.58). Correlations were found between global and local K associated with clinical behavioral data (executive function and memory assessments) and CSF biomarkers (t-Tau, Aβ-40, and Aβ-42). The results suggest that the cortical folding component, K, is a premature discriminator of healthy aging, Mild Cognitive Impairment, and Alzheimer's Disease, with significant differences within diagnostics. Despite the non-concomitant events, we found correlations between brain structural degeneration (K), cognitive tasks, and biochemical markers.