Gravity as perspective: a uniqueness theorem for the pentachoron

Power lines over water curve toward the horizon. We call it Earth's curvature and attribute it to gravity. But perspective lines on a sheet of paper also curve — and we recognise those as a projection from three dimensions onto two. We prove that gravity is the same phenomenon: the projection of a four-dimensional simplicial structure onto the three dimensions accessible to any internal observer.

Three empirical facts — three-dimensional perception, universal gravitational coupling, and observer homogeneity — are shown to require, uniquely, the complete graph K5 (the pentachoron) as the fundamental discrete event. The ten edges of K5 are identified with the ten independent components of the spacetime metric. The observer's blindness to the absent fifth vertex (proved in the companion paper P22) forces the ADM 3+1 decomposition: six visible edges become the spatial metric, three become the shift, and one becomes the lapse. This is not a gauge choice — it is a theorem of simplicial topology.

A single free parameter epsilon (the temporal edge perturbation) governs the entire gravitational chain: the dihedral angle, the lapse, the volume, and the Newtonian potential, with gravitational response coefficient (N-1)/N = 4/5. The Regge Hessian yields all ten linearized Einstein equations in ADM block form, with the Schlaefli identity enforcing the Bianchi identities. Cross-validation with the Planck gap formula ln(m_Pl/m_e) = 50 + alpha* u^16 yields Newton's constant at 0.29% from alpha* and m_e alone. The number 16 = 5^2 - 3^2 is the Pythagorean deficit between the whole (K5) and the part (the observer): gravity is what the observer cannot see.

All results are verified by a companion script (245tests, 0 failures).