Self-Referential Dynamics of the Damping Parameter: k(t) as an Emergent Process in the ASR Framework

We propose an extension of the ASR (Autonomous Self-Referential Universe) framework that formalises the dynamics of the damping constant k over cosmological time. Starting from the observation that the axiom U = F (U) naturally implies an analogous condition for k — namely k* = k (k*) — we derive a class of trajectories k (t) compatible with the principle of minimum entropy increase. The equation dk/dt = A· (k* − k), derived from an action functional with a potential emerging from the dimensional thresholds kₘ*, naturally produces: Nₑ ≈ 60 inflationary e-folds, a primordial spectrum with spectral index nₛ ≈ 0. 96, a tensor-to-scalar ratio r ≪ 1, and a distinctive observational prediction: micro-deviations in the CMB spectrum at logarithmically spaced scales (ℓ ≈ 10, 60, 200) corresponding to dimensional collapse thresholds. Inflation does not require an additional scalar field: it emerges as a geometric consequence of the potential V (k) built from the thresholds kₘ*. The weights wₘ of the potential are derived from the ASR axiom itself: wₘ = φ (φᵐ) ² = φ^ (−2mk*), forming a geometric series with ratio φ^ (2k*) ≈ 4. 12. The constant C mapping k-space to ℓ-space is anchored to the CMB observable window: C ~ ln (ℓₘax/ℓₘin) /k* ≈ 4. 7–7. 5. This is Paper 5 of the ASR series.