The Cosmological Constant as a Feedback Attractor

Three independent research programmes — Lombriser (2019, PLB), Farrah et al. (2023, ApJL), and Bonanno this density ratio is reported as an illustrative comparison, not a full Bayesian model selection. A stochastic-attractor demonstration shows convergence from four orders of magnitude of initial spread to 0.087 dex scatter in fewer than ten iterations. Scope and limitations. The framework proves existence and stability of the attractor but does not specify the physical coupling mechanism. The specific mechanism determines the precise elasticity but not the attractor’s existence. A companion paper (Paper II) proposes one candidate mechanism and derives testable predictions. Reproducibility. Full Python code reproducing all figures, numerical results, and sensitivity analyses is included in the bundle under CC BY 4.0. All code uses only standard scientific Python (NumPy, SciPy, Matplotlib). No fitted or calibrated parameters are introduced — all inputs are taken directly from the published sources cited above. Series. This is Paper I of a three-part series: Paper I (this work): mechanism-independent attractor theorem.Paper II (Salmond 2026, DOI: 10.5281/zenodo.20222173): test of a specific coupling mechanism (Connected Singularity Hypothesis) against DESI DR2 BAO data .Paper III (Salmond 2026, DOI: 10.5281/zenodo.20222352): UV–IR two-boundary determination connecting asymptotic safety to the IR attractor