Large Linear Cosmology and CMB/LSS Safety of the Mid–Band Portal in a 7D 2 time Principle of Least Information Constrained Universe

We formalise the linear–cosmology limit of the Janus/PLI mid–band portal and show
that if μ(a, k) obeys μ(k → 0) = 1 with derivative–suppressed tails, then primary CMB
acoustic physics and linear growth remain effectively ΛCDM–like, with sub–percent shifts
in Cℓ over 100 ≲ ℓ ≲ 1000 and in f σ8 at z ≲ 1. Our parameterisation and the safety thesis
follow the notation and motivation of Paper A and the foundations note (v14), where PLI,
strong positivity, and the hidden–time sector are laid out; see §§ 2–6 of Paper A and §§ 1–5,
8–11 of v14 for context and the positivity/Born machinery. We use standard cosmological
perturbation theory and Boltzmann codes as benchmarks