This work establishes the Spatial Pressure Gravitational Theory (SGT), an original, self-consistent, medium-dynamical theory of gravity, built rigorously from a foundational thought experiment—the Rubber Band Room—which motivates and anchors the entire theoretical framework. From this intuitive physical picture, we derive the nonlinear static field equation of SGT and provide six full mathematical self-consistency tests, unified explanations for nine key observational facts in gravitational physics and cosmology, three unique falsifiable predictions, and complete open-source Python numerical validation code that independently reproduces all theoretical results. This is a full, self-contained, testable, and verifiable theoretical system with complete mathematical and numerical support—not a conceptual or heuristic proposal. The theory postulates that the vacuum background is filled with a continuous, elastic, static Spatial Pressure Medium, and that gravity arises not as an attractive force, but as a "Spressure" gradient driven by medium displacement due to matter. In the strong-field limit, SGT reduces to Newtonian gravity and is consistent with the static predictions of general relativity. In the weak-field limit, it naturally produces flat galaxy rotation curves without dark matter and analytically derives the Baryonic Tully-Fisher Relation (BTFR). The theory also intrinsically predicts the External Field Effect (EFE) from its nonlinear structure. The nine observational facts unified by SGT include: the equivalence principle, the inverse-square law, the long-range nature of gravity, the equality of light and gravitational wave speeds, the absence of gravitational shielding, the spherical shape of massive celestial bodies, weightlessness in free fall, the conceptual consistency with the Casimir effect, and flat galactic rotation curves. All theoretical conclusions are validated by six mathematical self-consistency checks: weak-field BTFR derivation, nonlinear superposition failure and EFE, strong-field solar system compatibility, variational structure and conservation laws, numerical well-posedness, and cosmological order-of-magnitude consistency. The full Python code is provided to ensure transparency, reproducibility, and independent verification. This is a complete, formal, numerically validated, and observationally constrained framework for the fundamental origin of gravity. ( direct link )
