General Quantum Occupancy Theory (GQOT) - VOL V- Distance as Density of Correlation: Three Dimensions, Free Light and Continuous Colour as Survivors of Selection

General Quantum Occupancy Theory (GQOT) starts from a single postulate: a system cannot completely represent itself. This paper follows three ideas that come from that postulate. Distance is the density of correlation between nodes that have no positions. Clocks are nested: what an observer registers as one step is a short history of finer latent steps, and the structure repeats at every level. Nothing is fixed by rule: chronoentropic sorting keeps, from an immense deck of configurations, those that can persist. Simulating that selection in full is out of reach, but its survivors can be built from discrete records and tested for viability. Results Three dimensions. Counted correlations fall off as r^−(D−2), and bound structures of a stable, coupling-set size exist only for D = 3. Synchronisation rules out D = 2, and free light rules out 2+1. Continuous colour from discrete hops. A single coarse colour clock, a finite subgroup of SU(3), freezes before the continuum. When each registered colour link wraps a chain of three or more latent hops, the lattice reproduces continuous SU(3) to about ±0.002 in the plaquette across the scaling window, and the freezing point moves up with every hop added. Light and colour from one group. In Pati–Salam form the photon goes free while colour is still coarse. What light and colour share is the group structure that ties charges in thirds to colour triality. Space grown from a single origin. With records carried link by link, 2D growth stays flat, single-sheeted and seamless beyond a million clocks in eight of eight seeds. 3D and 4D growth are equally clean at the sizes tested, and bound structures on grown 3D space match a perfect lattice. In 3D every link must carry a twist, a discrete phase. The paper links these results to the single-aperture Big Bang, the Endocosmic Tilt and the black holes of GQOT Paper V (doi:10.5281/zenodo.20693412). It also sets out a picture of cosmic expansion as the uptake of nodes into the interior of grown space. The simulations test the survivors of selection, not the selection itself, and do not yet derive the gauge groups. Part of the GQOT series, following Observation as Overlap (doi:10.5281/zenodo.22959534), Emergent Locality from Observer Gluing (doi:10.5281/zenodo.23295512) and Phases and Particles from the Serialization of Change (doi:10.5281/zenodo.23377217). Code: the simulation code is deposited in a separate upload with DOI 10.5281/zenodo.24018999.