Circular Cosmology: Deriving Fundamental Constants from a Single Topological Axiom.

This is the corrected and fully reproducible version (v2.0) of the CosmicCircle framework. It contains: the main paper (CosmicCircle Paper A), the full mathematical derivations (Supplementary I–IV), the DESI DR1 comparison (Appendix A), the claim‑verification checklist (Preface), all code, data, logs, tests, and checksums required for full reproducibility. All dimensionless results (ΩΛ, Ωm, u₀, z₍crit₎, χ²/dof, α, K, sin2β) are strictly independent of H₀. All dimensional quantities (t₀, a₀, R_H, M_eq) scale with H₀. The DESI comparison uses rd‑free ratios and is therefore H₀‑independent.** This version corrects the internal inconsistency present in earlier releases (mixing two different H(z) formulations), which affected the values of z₍crit₎ and u₀. The issue is fully resolved here. All previous versions have been withdrawn for transparency. This package provides a complete, self‑contained reproducibility environment for the DESI DR1 analysis (χ²/dof = 0.751 for S³ vs 1.486 for ΛCDM), the topological invariants of S³, and the particle‑sector results. This version includes the Errata v2 (March 2026), correcting three presentation points and adding the updated Supplementary materials I–V Added: Addendum — The Arctan Curve, the Padé Approximant, and DESI Data. Clarifies that the CosmicCircle expansion law is the arctan curve a(u) = 1/√(1+u²), derived exactly from S³ topology (Arctan Lens Theorem, Paper C). The Padé approximant is not an approximation to this law but a corrector for the ΛCDM prior introduced in DESI data preprocessing. The Padé coefficients measure the distortion introduced by the ΛCDM pipeline, not free physical parameters. Key falsifiable prediction: z_crit = 0.6259 (S³) vs 0.6702 (ΛCDM) is testable with DESI DR3 in two independent ways — standard pipeline and model-independent non-parametric fit. Corrective Addendum (March 2026) This version includes a formal corrective addendum clarifying the logical role of the Wyler geometric number and retracting the previously stated prediction z₍crit₎ = 0.6259. The retraction does not affect any derived results of the framework: the predictions for H₀, Ωₘ, and w = –1 remain unchanged and follow directly from proved theorems. The addendum documents the correction transparently and replaces the withdrawn value with the framework’s genuine falsifiable predictions.