The Curved-and-Finite Universe Hypothesis (CFUH-S) is a prospective, falsifiable cosmology paper that converts a broad structural intuition – that the large-scale Universe may be both curved and finite – into a conventional observational hypothesis with explicit failure conditions. The paper does not claim that current data establish a closed Universe. Instead, it freezes a minimum-effect branch before future adjudication so that the claim cannot retreat toward exact flatness after new observations become available.
The registered hypothesis is CFUH-S: the present-day curvature density parameter satisfies Omega_K,0 <= -1.0 x 10^-3 under the standard convention Omega_K,0 = -k c^2/(a0^2 H0^2), where positive spatial curvature corresponds to Omega_K,0 < 0. In the homogeneous and isotropic branch used for primary testing, spatial slices are compact spherical space forms S^3/Gamma. For the simply connected S^3 branch, the curvature radius and finite spatial volume follow directly from Omega_K,0 and H0.
The paper separates three issues that are often conflated: geometric curvature, global topology, and finite spatial volume. It also explicitly separates the information-first motivation from empirical evidence. Unified Informational Physics and Unified Informational Mathematics are used only to motivate and organize the candidate geometry. The observational claim is judged by standard cosmological measurements and can be rejected by them.
Current evidence is treated adversarially. Final Planck PR4 analyses are consistent with flatness. DESI DR2 Results IV, using Lyman-alpha full-shape information together with BAO and CMB data, reports 10^3 Omega_K = 2.1 +/- 1.1, a mild approximately 2 sigma preference in the open-direction sign while remaining consistent with flatness. As of 29 September 2026, the DESI paper remains arXiv:2607.27410v3 with no journal reference listed on arXiv; the official DESI DR2 publications page lists it as a key publication.
CFUH-S is therefore not presented as confirmed. The paper defines prospective support, falsification, and inconclusive outcomes. Decisive falsification requires curvature precision sigma(Omega_K) <= 2 x 10^-4, at least 5 sigma exclusion of the registered boundary, strong model-comparison evidence, robustness to non-flat evolving-dark-energy models, replication across independent probe families, and satisfactory residual/integrity checks. Support requires an equally stringent negative-curvature-density result that lies decisively inside the registered CFUH-S region and survives the same alternatives.
This deposit includes the final manuscript, a versioned reproducibility repository, machine-readable decision rules, unit tests, source manifests, a falsification schematic, and public-communication materials. The code reproduces the manuscript-specific calculations and adjudication layer and accepts reviewer-supplied public Omega_K chains. It does not claim to reproduce the complete external Planck or DESI likelihood pipelines.
The reproducibility layer is intentionally modest in scope. It verifies the manuscript’s own geometry calculations, Gaussian diagnostic distances, decision thresholds, and branch classification, while keeping externally produced cosmological likelihoods outside the repository’s evidentiary ownership. This prevents a common category error in independent analyses: presenting literature-transcribed constraints as if they were newly measured. Reviewers can replace the summary constraints with official public posterior chains through the included chain adapter and then apply the same frozen CFUH-S classifier. All repository files are checksummed, and the verification script produces a machine-readable pass/fail report.