Discovery Plane Theory in Practice: A Complete Worked Guide to Scientific Question Evaluation, Discovery Complexity, and Question Compression

This educational guide provides a complete worked implementation of Discovery Plane Theory (DPT) through a fully reproducible university energy-research example. The manual demonstrates, step by step, how scientific research questions can be systematically generated, evaluated, compared, and selected using the two fundamental coordinates of Discovery Plane Theory: Discovery Complexity (DC) and Question Compression (QC). Beginning with a declared Reality Space and Background Knowledge, the guide illustrates every stage of the DPT workflow, including Discovery Complexity calculation, Question Compression estimation, Discovery Plane coordinate construction, region classification, dominance analysis, Discovery Frontier extraction, research-budget constraints, weighted discovery distance, geodesic analysis, utility evaluation, sensitivity analysis, dynamic coordinate interpretation, and final research-question selection. Unlike a theoretical exposition, this guide presents every calculation manually with detailed explanations, mathematical formulas, worked tables, figures, and practical interpretations. It is intended to support researchers, faculty members, PhD scholars, postgraduate students, research supervisors, and research committees who wish to understand or teach Discovery Plane Theory through a transparent and reproducible example. The guide complements the formal DPT framework and computational benchmark by translating the mathematical theory into a classroom-ready implementation that can be adapted to diverse disciplines, including engineering, computer science, management, medicine, education, law, social sciences, and the humanities.