Testing a Connected-Singularity Mechanism for Gravitational Feedback Cosmology

Within the feedback-attractor framework of Paper I (Salmond 2026, DOI: 10.5281/zenodo.20156389), which proves that any cosmology with negative feedback between Λ and structure formation has a unique stable fixed point, this paper proposes and tests the Connected Singularity Hypothesis (CSH): a cyclic cosmology in which black-hole interior boundaries are topologically identified with the Big Bang boundary via a cobordism on S³. Observational inputs. The analysis uses DESI DR2 BAO measurements (5 anisotropic + 1 isotropic bin, April 2025 public release), the Planck 2018 CMB distance prior (r* = 147.05 Mpc, z* = 1089.8), the Madau & Dickinson (2014, ARA&A 52, 415) cosmic star formation rate, Planck 2018 cosmological parameters, and LQC bounce parameters from Ashtekar, Pawlowski & Singh (2006) with Barbero-Immirzi parameter γ = 0.2375. Main results. The CSH admits two physically distinct readings. Reading A (live BH mass sourcing) makes a sharp, parameter-free structural prediction: w = −1.09 ± 0.04, derived from the Madau-Dickinson SFR with zero free parameters. A joint BAO + CMB likelihood analysis using DESI DR2 data disfavours Reading A at 4.5σ. This falsification is reported honestly and in full — the prediction was testable, was tested, and the result is informative: it constrains the boundary identification to operate atemporally (Reading B), not as a live source within a cycle. Under Reading B (w = −1 exactly, ΛCDM background), three signatures are identified: (1) a σ₈–Λ joint constraint with slope ≈ 1.4; (2) population-level BH parameter uniformity testable with GWTC-4; (3) a LISA primordial gravitational-wave spectral feature. Structural caveats for each are given explicitly. Scope and limitations. The framework of Paper I survives regardless of the CSH’s fate. The CSH is one instance of the broader feedback-attractor class; if the CSH is wrong, the attractor theorem holds and other mechanisms remain viable. The paper’s most informative result is arguably the falsification of Reading A, which demonstrates that the framework generates predictions sharp enough to be ruled out by data. Reproducibility. Full Python code reproducing all figures, likelihood analyses, cobordism computations, and energy-ledger calculations is included under CC BY 4.0. The DESI DR2 data points used are tabulated in the code headers. All code uses standard scientific Python. Series. This is Paper II of a three-part series: - Paper I (Salmond 2026, DOI: 10.5281/zenodo.20156389): mechanism-independent attractor theorem - Paper II (this work): CSH mechanism test against DESI DR2 - Paper III (Salmond 2026, DOI: 10.5281/zenodo.20222352): UV–IR two-boundary determination connecting asymptotic safety to the IR attractor