The Joint Run: Pre-Registration for the First Simultaneously Normalized MCMC Sampling of k_E, λ_V, and β_m Against the Full Planck 2018 + Pantheon+ + DESI BAO Likelihood

Pre-registration for the first joint MCMC run in the Living Theory of Everything (LTOE) series in which the three cosmological coupling parameters k_E (coherence coupling), λ_V (scalar potential slope), and β_m (conformal coupling) are sampled simultaneously as free variables. Data: Planck 2018 TT+TE+EE + Pantheon+ SNIa + DESI BAO 2024. Sampler: Cobaya, Metropolis-Hastings, ≥8 independent chains, convergence target R̂−1 < 0.01. Five predictions locked before any chains run: (P1) k_E consistent with Phase 6 result 1.923+0.28/−0.40; (P2) joint posterior either finds unification k_E ≈ λ_V ≈ β_m or three independent constraints — both outcomes pre-registered; (P3) λ_V MAP ≈ 1.045 confirmed or revised; (P4) β_m consistent with x_m = 0.026 (Paper LXXIII); (P5) full convergence. Builds on Paper CVI (DOI: 10.5281/zenodo.21304192) and Paper LXXIII (DOI: 10.5281/zenodo.21121889). Paper CVII of the LTOE series.