Quantum Gravity within the OTIS Framework: Black Hole Entropy, Generalized Uncertainty Principle, and the Graviton from the Octonion Hierarchy

Three results in quantum gravity are derived within the OTIS (General Theory of Hierarchical Synthesis) framework. The coefficient 4 in the Bekenstein–Hawking entropy formula S = A/(4lPl²) is derived from the quaternion algebra dimension dim(ℍ) = 4 — the first derivation of this coefficient from first principles. The generalized uncertainty principle (GUP) parameter is fixed at β = 1/N₂² = 1/441 from the Fano plane geometry — the first parameter-free prediction of β from geometric first principles. The graviton is identified as a coherenton of the base level Ξ₀ — the minimal three-element directed cycle of OTIS Axiom 3 — which ensures its necessary masslessness, consistent with the experimental bound m_graviton < 1.27×10⁻²² eV. Part of the OTIS series (DOI: 10.5281/zenodo.19160535).