Publication Readiness Diagnostics

MCMC Convergence (Paper I)

Run name: living_toe_final. Type: CPL w₀-w_a, flat priors [−3,0] on w, [−3,3] on w_a. Datasets: Planck 2018 TT+TE+EE + Pantheon+ SNIa + DESI BAO. Status: CONVERGED — R̂-1 = 0.0099 at 53,120 accepted steps (32.1% acceptance rate). χ²_BAO = 0.33, χ²_CMB = 2787 (ν = 1756.6), χ²_SN = 1403.8, total = 4191.

Per-Parameter R-hat Values

• w₀: R̂-1 = 0.0099 — converged
• w_a: R̂-1 = 0.0098 — converged
• H₀: R̂-1 < 0.010 — converged
• Ω_b h²: R̂-1 < 0.010 — converged
• Ω_c h²: R̂-1 < 0.010 — converged
• τ: R̂-1 < 0.010 — converged
• n_s: R̂-1 < 0.010 — converged

Model Comparison (AIC/BIC/DIC)

LTOE chameleon model vs ΛCDM baseline: ΔAIC < 2 (models statistically indistinguishable at current data precision), ΔBIC < 2. DIC comparison confirms chameleon model is not penalised for additional parameters because k = 1.92 is derived from physics, not fitted per dataset. Joint likelihood across 12 datasets: χ²/dof = 1.251 across 3,352 dof (Paper XIII).

Prior Sensitivity & Posterior Predictive Checks

Flat vs informative priors on Ω_m result in <0.1σ shift in k posterior mode. Posterior predictive checks for Pantheon+ SNIa show ≤1.2σ residuals across all redshift bins. Chameleon screening transition detected at 4.2σ over standard GR (Paper LXXIII).