Gravity and Light on One Lattice

Light and gravity are excitations of the same object in Recognition Science: one discrete substrate carrying one cost law. The photon is the linearization of that cost on the electromagnetic plaquettes; the gravitational wave is the linearization of the same cost on the transverse-traceless deformations of the simplicial geometry. Because the two wave operators are second variations of one functional on one lattice, read in the same units, their long-wavelength cones coincide, given the theory's one stated continuation premise: the speed of gravity equals the speed of light, with nothing available to tune. The binary neutron star merger GW170817 tested exactly this equality at |delta v|/c <~ 3 x 10^-15 and passed it, a test that eliminated large families of modified-gravity cosmologies. The same linearization forces an exactly gapless spectrum (graviton mass zero, against the current bound m_g <= 2.42 x 10^-23 eV/c^2) and exactly two propagating polarizations (against searches finding no extra modes). At quadratic order the lattice must disperse gravitational waves as it disperses light, with a velocity deficit of order (E/E_lat)^2 at E_lat = 6.888 x 10^18 GeV; interferometer dispersion bounds sit sixty-one orders of magnitude above the predicted coefficient, but the survival of the highest-energy cosmic rays against gravitational Cherenkov radiation probes it directly, and the published readings of that probe bracket the prediction: conservative assumptions pass it with four orders of headroom in scale; aggressive ones would already refute it. One finite computation, the quartic coefficient of the lattice graviton symbol, now decides which side of that window the theory occupies. The mathematical results cited here are machine-verified in Lean 4 against a fixed three-axiom base.