This monograph provides in-depth mathematical logic as the foundational rationale for the novel and innovative online instructional methodology called the 4A Metric Algorithm. The 4A Metric has been designed to address and meet the meta-competency-based education challenges faced by 21st century students who must now adapt to and learn in a multitude of educational settings (face to face, hybrid, and online). The 4A Metric has a geometrically-spatial infrastructure that mathematically defines its unique online "E-Learning Engineered" methodology for online information delivery. This methodology is defined as a "Quadrilateral Function of E-Learning Engineering" that is grounded in neuroscience of mathematical trichotomy and the "neuromeasurement" of the "Bi-coordinate Scale of Learning". The 4A Metric as an instructional methodology detailed in this narrative also provides an active solution that when implemented via an institutional Learning Management System (LMS)/Content Management System (CMS) uses virtual methods to achieve maximized information delivery in terms of meta-competence-based education for online learning. The explicative nature of the "Quadrilateral Function" also adds further mathematical value to online learning investigative inquiry through measurement, the efficacy of digital instrumentation, and information gathered through tools developed specifically for eduscientifically-engineered (Osler, 2013a and 2013b) research designs (Osler, 2013b and 2015a).