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. https://dfife.github.io/index.html v2.0 (May 2026): Bundle release, conventions standardization, and §11 closure. Status labels and supporting metadata standardized to the framework conventions in conventions_v2.md (https://github.com/dfife/io-framework-public/blob/main/docs/conventions_v2.md). §11 rewritten: the Boundary Fixed-Point Principle (Reconstruction in v1.3) is superseded by Definitions 28.FC1–28.FC2 and Theorem 28.FC6, which prove that the physical primordial scalar covariance belongs to the multiplicative Dirichlet-to-Neumann (DtN) fixed-point class on the active reduced scalar-source block (Derived / Conditional-Verified). The closure terminates in Premises P1 and P2, Papers 18, 23, 25, and 32, and Paper 28's own operator-structure theorems, with the Barbero-Immirzi parameter as the only imported empirical input. Paper 32 v1.6 supplies the previously established theorem-grade dependencies: Theorem 32.B and Corollary 32.B.1 (typed boundary-to-bulk projection / source-block identification), Theorem 32.KB.7 (DtN open-transport placement), Theorems 32.KB.8 and 32.KB.5 (active source-block exhaustion and source-object lock), Theorem 32.A with Corollary 32.A.1 (modular-DtN field transfer and direct fixed-point closure), and Corollary 32.KB.3b (source exponent closure). Theorem 28.10 is re-anchored to the same source-block scope. §17.10 (Scope Note) adds an explicit closure framing for the formation-clock map: the homogeneous Oppenheimer-Snyder formation-clock map is DERIVED/THEOREM (Theorem 28.11); the projected/readout clock as a local formation clock is DERIVED/NO-GO; and inhomogeneous object-specific corrections are characterized as outside the active claim scope, not as an open gap. Reproducibility bundle: https://github.com/dfife/io-framework-public/releases/tag/paper28-v2.0 (tarball SHA256 75b1bdcf90a6fed53631a5c25838e28b7cf3205e979c2717f9a87bdbded5a4d6). Validation: 13/13 reproducibility checks pass. v1.3 (April 2026): Rebuild audit. Appendix replaced with Paper 27 v1.5 clean chain + Paper 28 theorems (theorem-grade only). A.0 Master Mathematical Reference replaced with formatted Word table. Dead values purged from A.0 (P_k = 0.0601, H₀ = 68.91 Schur rows removed). §11.4 rewritten: sole-survivor language removed, Boundary Fixed-Point Principle justified as semiclassical principle with elimination record as motivation. Open/Closed tracking added. Open Problems updated: PSRP and Boundary Covariance Exponent replaced by Boundary Fixed-Point Principle. Appendix hygiene: correction notes cleaned (Steps 26, 95), scorecard blocks removed (Paper 19/20 Key Numerical Values), kill-list steps removed (373–375), all STATUS: DERIVED/NO-GO labels corrected to DERIVED, Step 20 status label trimmed. Cosmetic: Schur definitive→conditional Schur, Rosetta→gauge partition. Schur branch retirement noted in Steps 54, 98. v1.2 (April 2026): Master clock correction. The OS dust cycloid is replaced as the master clock by the bare-branch mixed-fluid K=+1 FRW proper-time integral t_bare(z) = integral from z to infinity of dz'/[(1+z')H_bare(z')], which includes dust, radiation, curvature, and the cosmological constant from Einstein-Cartan-Holst torsion. The correct local-clock age is t_bare(0) = 19.181 Gyr (not 33.36 Gyr from the dust cycloid, which approaches a fictional turnaround that the cosmological constant prevents). The dust cycloid is within 1% of the master clock only for z = 4.7 to z = 9.5; the old 0.03% convergence claim compared cycloid to radiation-neglected bare FRW, not the correct integral. Radiation density corrected: Omega_r,bare = 1.226e-4. Section 1 corrected: closed but non-recollapsing. Section 17 rewritten with correct master clock formula and table. The 46% extra JWST formation time remains valid in the matter era (z ~ 5-50); the true high-z asymptote is t_bare/t_LCDM to 1.0003 (radiation era). Theorems 28.1-28.11 are unaffected. v1.1 (April 2026): Paper 29 branch consistency audit. Step 440 updated: projected branch corrected from mixed (H₀ = 67.58) to Schur definitive (H₀ = 68.91). Appendix B numerical values updated to Schur branch (Ω_m = 0.336, Ω_Λ = 0.670). Appendix C updated with Paper 29 closures (assembly gap, BAO residual). All component theorems (Parts I–V, Theorems 28.1–28.11) are unaffected.