The Interior Observer Cosmological Framework — Paper 28: The Primordial Spectral Index, the JWST Impossible Galaxy Tension Eased, IO-Native Scale Invariance, the DtN Boundary Hessian, and the Boundary Fixed-Point Principle

Beginning from two premises — (1) the observable universe exists inside a Schwarzschild black hole, and (2) the physics inside the horizon is the same as outside — Paper 28 builds a substantial theorem scaffold for the primordial scalar power spectrum, introduces one new semiclassical principle, and derives a homogeneous OS proper-time formation-clock theorem that conditionally alleviates the JWST "impossible galaxy" tension.

The spectral index n_s = 1 − K_gauge/x = 0.9639 (0.24σ from Planck, zero fitted parameters) is obtained through eleven new theorems — including the Hawking Accumulation Theorem (IO-native scale invariance from N³ × N⁻³ cancellation on the OS cycloid), the DtN Boundary Hessian identification on the Painlevé-Gullstrand collar (σ_ℓ = (ℓ+1)/r_s, matching Karpukhin's published Steklov eigenvalues), and the Shell-Dependent Zeroth-Order Exclusion Theorem — plus one new Boundary Fixed-Point Principle that replaces the Paper 23 PSRP and Boundary Covariance Exponent with a single, sharper anomalous-dimension identification in standard RG language. Twenty-three alternative mechanisms for the spectral tilt are tested and killed.

The Homogeneous OS Formation-Clock Theorem (Theorem 28.11) proves via the equivalence principle that local structure formation runs on OS cycloid proper time, not on the projected FRW age inferred from photon measurements. The exact formula τ(u) = (r_s/2c)[arccos(1−2u) − 2√(u(1−u))] with u(z) = 1/(x(1+z)) gives 46% more physical formation time than ΛCDM at all z > 10 (asymptotic ratio 1.460, zero parameters). For JADES-GS-z14-0 at z = 14.18: 431 Myr vs ΛCDM's 291 Myr. This result is independently confirmed by the bare-branch Friedmann integral, which converges to the OS proper time at high z with ratio 1.000327. No framework observable (T_CMB, θ_s, BBN, n_s, A_s) depends on the late-universe age-redshift relation, so using the OS clock creates no conflict with existing predictions.

All results validated by independent multi-AI adversarial review. No parameters are fitted to cosmological data.