The Structural Necessity of Attractive Gravity: Formal Proof and Pedagogical Perspectives

This package explores the sign of the gravitational constant ($G$) not as an empirical contingency, but as a structural prerequisite for the existence of persistent physical systems. Using the Raychaudhuri equation and standard energy conditions, we argue that a repulsive gravity framework ($G < 0$) leads to global geodesic defocusing, rendering bound states, observation, and time-evolution mathematically incoherent. The package includes three documents: 1. attractive_gravity_paper.pdf (The Formal Proof) - A rigorous, standard-format physics paper demonstrating that repulsive gravity prohibits the formation of caustics and bound worldlines. - Key arguments: Raychaudhuri defocusing, Newtonian potential instability, absence of stable geodesics. 2. so_you_think_you_know_gravity_v1.pdf (The Pedagogical Primer) - A conversational, Feynman-style introduction to the concept. - Designed for broad accessibility, explaining why "turning the gravity knob to the left" results in a universe without observers. 3. so_you_think_you_know_gravity.pdf (The Deep Dive / V2) - An expanded pedagogical treatise that bridges the gap between the primer and the formal proof. - detailed analysis of "The Universal Solvent" (atomic dissolution) and "Thermodynamic Death" (entropy in a defocusing geometry). - Explicit discussion of the "silence" in standard general relativity textbooks regarding this constraint.NOTES:This work challenges the implicit assumption that the attractive sign of gravity is merely an observational fact, proposing instead that it is a consistency condition for any metric theory admitting variational motion.