Chapter 3: The Iterator ρ and the Omega Beacon

We introduce ρ, the sole ontic operator of Category τ. The operator ρ acts as a progression (successor) on each generator, unfolding the infinite orbit rays that populate the universe. Two kernel axioms govern its behaviour: K2 declares ω the unique fixed point of ρ, and K5 asserts that ω is unreachable — no finite iteration of ρ on any other generator ever reaches ω. Together, these axioms establish the beacon: a fixed horizon that bounds the universe from above without belonging to any orbit ray.