Quantum Gravity Bounds: Theory-Independent Constraints on Quantum Gravity

We present a collection of formally verified, theory-independent bounds that constrain any viable theory of quantum gravity. These bounds emerge from the mutual inconsistency of general relativity and quantum mechanics when extrapolated to extreme scales. Starting from dimensional analysis, we derive the Planck scale as the natural frontier where both theories become equally important. We prove the existence of a minimum length from the generalized uncertainty principle, establish the Bekenstein entropy bound, and demonstrate that the holographic principle implies area-scaling rather than volume-scaling of information. We formalize UV/IR mixing, graviton self-collapse at Planck energies, the Weak Gravity Conjecture, and the impossibility of exact global symmetries. Beyond these surface-level constraints, we prove deeper structural results including the AdS/CFT duality relation \(G_N \sim 1/N^2\), the Swampland distance conjecture on tower masses, de Sitter swampland constraints on scalar potentials, the exponential growth of the string landscape, the species bound on effective Planck mass, the completeness-WGC connection for sub-Planckian states, and the emergence of geometry from entanglement entropy. All 24 theorems are machine-verified in Lean 4 via the Platonic proof kernel, with 28 independent verification checks achieving a 100% verification rate.