ΩCDM: A Pre-Registered Cosmological Prediction — Ω_Λ = ln 2 as a Fixed Constant

ΩCDM: the dark-energy density parameter is a fixed constant, ΩΛ = ln 2 = 0.6931472, rather than a fitted quantity — a cosmology with one fewer free parameter than ΛCDM. What is deliberately NOT registered. The agreement of ln 2 with Planck 2018's ΩΛ = 0.6847 ± 0.0073 (a +1.16σ offset) is not filed as a prediction. That value was measured before this filing, so claiming it would be backdating. This applies the same rule that withheld a0 = cH0/2π from the v2 predictions deposit (10.5281/zenodo.21864057) on the grounds that it had already been tested against SPARC and was therefore a retrodiction. Registered. P1 — H0 = 68.27 km s-1 Mpc-1, derived from flatness plus ΩΛ = ln 2 (giving Ωm = 1 - ln 2 = 0.306853) and the CMB-measured ωm = 0.1430; falsified by a converged H0 ≥ 71. P2 — Ωm = 0.306853 exactly. P3 — the directional bet, and the substantive registration: as precision on ΩΛ improves, the central value moves toward ln 2 rather than remaining at 0.6847. This is not knowable at filing time. A measurement at σ ≤ 0.0028 (CMB-S4 reach) returning a central value at or below 0.6847 puts ln 2 at 3.02σ and falsifies the model outright; no tunable parameter is available. P4 — w = -1 exactly and wa = 0, since a fixed horizon property admits no evolution; testable now at σ(w) ~ 0.02. Stated against our own interest. The two headline quantities of this programme are not jointly satisfiable at a single H0: ΩΛ = ln 2 requires H0 ≈ 68.3, while a0 = cH0/2π sits closest to the MOND scale at H0 ≈ 73, where ΩΛ would be 0.7320 — about 5σ from ln 2. A converged H0 measurement therefore kills at least one of the two. This is recorded as a falsifiable consequence rather than resolved by selecting a different H0 per claim. Assumed, not derived. (i) The ln 2 itself, motivated as one binary horizon degree of freedom — a Landauer/Shannon quantity, and explicitly not contained in the Bekenstein bound, which carries no ln 2. (ii) The length choice: the chain closes to exactly ln 2 only if the relevant length is the de Sitter curvature radius Λ-1/2 = c/(√3 H0); the Hubble radius c/H0 would give ln2/3 = 0.2310, which observation excludes. Nothing derives this choice. (iii) Epoch: ΩΛ(z) = ln 2 holds only for -0.026 ≤ z ≤ 0, an interval of about 0.39 Gyr or 2.8% of the present cosmic age. The model selects an epoch as well as a value and inherits the coincidence problem in full. No resolution is claimed. Priority. The relation 2πa0 ≈ cH0 ≈ c²(Λ/3)1/2 is Milgrom's (Phys. Lett. A 253, 273, 1999; Fortschr. Phys. 65, 1600046, 2017) and no priority is claimed for it. No prior publication of ΩΛ = ln 2 was located in a search of arXiv and Crossref; that is a statement about the search, not a claim of novelty. Reproduction. python3 verify_omegacdm_prediction.py recomputes every value at runtime from published Planck 2018 and SH0ES 2022 inputs. There are no hardcoded pass flags: each verdict is a comparison performed in-process, and a check that cannot be computed prints UNCOMPUTED rather than PASS. AI-use disclosure. AI systems assisted drafting and symbolic checking under direction. They are not authors, are not co-signatories, and performed no peer review. No AI verdict or self-issued "verification" appears in this deposit as evidence.