This work presents a scale‑invariant cosmology built entirely from ln 2 geometry. The model reveals a set of fixed‑point relationships linking cosmic time, radius, curvature, rotation, entropy, information, the Hubble rate, and the cosmological constant. These invariants hold for any choice of initial conditions, demonstrating that the geometry is renormalisation‑symmetric and independent of the seed scale. Key results include the expansion identity R=cT, the curvature relation k c T=1, the Hubble fixed point H T=ln2, and the cosmological‑constant invariant ΛR²=3ln2/ (1−ln2) ². The model also establishes a dual‑clock structure connecting cosmic time (the speed‑of‑information clock) with local proper time through a simple ln 2 conversion factor. All physical quantities scale by fixed ln 2 multipliers under renormalisation of the seed time, while the invariant combinations remain unchanged. The resulting structure is mathematically simple, internally consistent, and fully determined by the ln 2 ladder. The geometry itself defines the universe; the initial scale is merely a choice of units.
C Burton (Sat,) studied this question.