The Cosmological Constant as a Gravitational Feedback Attractor: A Universality Theorem and Candidate Mechanism.

We prove that any cosmology in which dark energy suppresses the formation of gravitationally collapsed structures that in turn contribute to dark energy possesses a unique, stable fixed point for the cosmological constant Λ. The fixed point's existence follows from the intermediate value theorem; its uniqueness from monotonicity of the structure formation function. When the coupling amplitude falls within a broad range around the structure formation transition scale Λ ~ Ω_m H₀²/c² ≈ 10⁻⁵² m⁻², the fixed point lies near the observed value. We derive the sensitivity of the fixed point to the coupling constant: d(ln Λ*)/d(ln κ) = 1/(1 − g′(Λ*)) ≈ 0.45, demonstrating sub-linear dependence that requires the coupling to be specified only within approximately two orders of magnitude. This suggests the observed Λ may be a feedback attractor rather than a fine-tuned parameter. This universality theorem unifies and explains several recent independent results: Lombriser's (2019) backreaction derivation of Ω_Λ = 0.704, Farrah et al.'s (2023) observational evidence for BH–Λ coupling, and Bonanno & Reuter's (2001) self-adjusting RG fixed point. Each found the same Λ through different mechanisms because the fixed point is a topological feature of the feedback, not a consequence of any specific physics. The coincidence problem (why Λ ~ ρ_matter now) is simultaneously resolved: the fixed point is defined by their balance. We further propose the Connected Singularity Hypothesis (CSH) as one candidate mechanism for the coupling, in which the future boundaries of all black hole interiors and the past boundary of the Big Bang are topologically identified as the same structure. This cyclic framework provides a natural physical basis for the coupling but is not required by the universality theorem.