Hybrid 5D Gravity (H5DG)

This paper investigates whether a universal low-acceleration scale, analogous to that of Modified Newtonian Dynamics (MOND), can emerge from a purely geometric five-dimensional braneworld framework. Adopting a deliberately minimalist philosophy, the model considers a single four-dimensional observer brane embedded within a warped bulk, governed initially only by the Einstein--Hilbert action and a negative cosmological constant. The analysis shows that minimal five-dimensional Einstein gravity naturally generates a characteristic geometric acceleration scale proportional to the de Sitter curvature of the boundary, but does not uniquely determine its numerical value. This limitation is traced to an undetermined boundary modulus arising from the classical Israel junction conditions, which leave the brane tension as a free parameter. The paper identifies this "Einstein Boundary Modulus" as the precise mathematical obstruction preventing the minimalist framework from making a parameter-free prediction. Rather than presenting a completed unified theory, the manuscript establishes a mathematically defined geometric research programme, identifies the point at which minimal Einstein gravity ceases to be predictive, and motivates higher-curvature extensions, such as Lovelock or Gauss--Bonnet gravity, as purely geometric mechanisms for dynamically fixing the boundary conditions. Throughout, established results, original derivations, conjectures, and open mathematical problems are explicitly distinguished using an epistemic status framework to maximise mathematical transparency.