We present Undecion (or Rolandion) Algebra, a mathematically rigorous 11-dimensional algebraic framework designed to bridge quantum mechanics and general relativity. Unlike previous approaches that struggle with mathematical consistency or experimental testability, our framework provides: (1) a precise scale-dependent product that smoothly interpolates between quantum and classical regimes, (2) well-defined dimensional transfer operators with proven conservation properties, and (3) a categorical foundation ensuring structural coherence across scales and dimensions. We develop the complete algebraic structure with explicit multiplication rules, provide formal proofs of key mathematical properties, and establish connections to established physical theories. The framework naturally addresses long-standing puzzles including the black hole information paradox, dark energy, and quantum measurement, without introducing ad hoc constructions or excessive free parameters. Most significantly, we derive specific, quantitative predictions testable with current or near-future technology: gravitationally enhanced quantum tunneling ($\Delta\Gamma/\Gamma \approx 10^{-8}$ for realistic laboratory parameters), neutron interferometry phase shifts ($\Delta\phi \approx 10^{-7}$ rad), modified Casimir forces (0.5\% deviation at 10 nm separation), gravitational wave dispersion, and an oscillatory dark energy equation of state ($w(z) = -1 + 0.03\sin(\pi z/(1+z))$). We provide detailed experimental protocols with sensitivity analyses demonstrating feasibility with existing techniques. The Rolandion framework thus establishes that quantum gravity phenomena need not be confined to inaccessible energy scales but can manifest in measurable effects at laboratory scales through dimensional transfer mechanisms.