P != NP: Five Independent Foundations of Computational Complexity

11×17 inch infographic on P ≠ NP and the Intrinsic Operational Gradient Theorem (IOGT).Five Primary Sections:Counting Asymmetry (Top Left) - Shows how construction precedes verification in arithmetic, with a visual number line demonstrating forward vs. backward countingInformation Theory (Top Right) - Binary tree visualization showing 2ⁿ exponential growth, with Shannon's bound equation (H ≥ log₂(k) bits)Thermodynamics (Middle Left) - Landauer's Principle (W ≥ kᴃT ln(2)) with branching energy cost visualizationCategorical Freeness (Middle Right) - Shows how operations form a Free TSMC with multiple distinct paths that cannot be collapsedEmpirical Universality (Right Column) - Evidence from 50 years of research, quantum limits, biological evolution, human cognition, and mathematical practiceKey Equations Featured:Cost(forward) = O(n) ≠ Cost(reverse) = Ω(2ⁿ)H ≥ log₂(k) bitsW ≥ kᴃT ln(2)W ≥ kᴃT·log₂(k)Conclusion Section: Three-panel analysis comparing abstract vs. physical computation, with implications clearly stated.