Testing a Connected-Singularity Mechanism for Gravitational Feedback Cosmology

Within the feedback-attractor framework of Paper I (Salmond 2026, The Cosmological Constant as a Feedback Attractor; hereafter Paper I), which proves that any cosmology with negative feedback between Λ and structure formation has a unique stable fixed point, we propose the Connected Singularity Hypothesis (CSH): a cyclic cosmology in which black-hole (BH) interior boundaries are topologically identified with the Big Bang boundary. The CSH admits two physically distinct readings — live identification (Reading A: Λₑff sourced in real time by accumulating BH mass) and cycle-boundary identification (Reading B: Λ fixed at the Big Bang by the previous cycle). Reading A makes a sharp, parameter-free structural prediction: ρDE (z) /ρDE, 0 ≤ 1 for all z ≥ 0, with local equation of state wₑff (z=0) = −1. 09 ± 0. 04 (phantom, derived from the Madau Reading A's structural ceiling lies in the half-plane opposite to DESI's preferred ρDE (z=1) /ρDE, 0 ≈ 1. 21, confirming it could not have been constructed to accommodate the data. A joint baryon acoustic oscillation (BAO) + cosmic microwave background (CMB) analysis disfavours Reading A at 4. 5σ — the prediction was falsifiable, was tested, and the falsification is informative: it constrains the BH–Big Bang boundary identification to operate atemporally at cycle boundaries, not as a live source within a cosmic cycle. The framework is therefore developed under Reading B (wₑff = −1 exactly, ΛCDM background to leading order). Three signatures distinguish the resulting framework from standard ΛCDM: (F3) a σ₈–Λ joint constraint d ln Λ/d ln σ₈ ≈ −1. 4, partially tested by Dark Energy Survey (DES) Y6 (S₈ = 0. 789 ± 0. 012, 1. 8σ below CMB) and approaching the decisive DESI-DR2 × DES-Y6 test; (C3) population-level uniformity in LIGO–Virgo–KAGRA (LVK) BH parameters beyond population-synthesis predictions, testable now with the Gravitational-Wave Transient Catalog (GWTC-4) ; and (C4) a Laser Interferometer Space Antenna (LISA) primordial gravitational-wave (GW) spectral feature at f* ∈ 10⁻⁵, 10⁻³ Hz (target: LISA Y1, ~2035–2037). F3 and C3 carry structural caveats: F3's Press–Schechter slope (−1. 4) is degenerate with the ΛCDM data-projection slope (~−1. 3) from the S₈ weak-lensing degeneracy; C3's population-level signal reduces to a cumulative-mass anchor that is degenerate with current astrophysical extrapolation uncertainty (~2 dex) at GWTC-4 sensitivity. Both are retained as registered predictions deferred to power-adequate tests; C4 remains the framework's distinctive forward-looking empirical content. The framework of Paper I survives regardless of the CSH's fate.