Relational Actualism Gravity and Cosmology

his paper formalizes the extension of Relational Actualism (RA) into the non-inertial and curved spacetime regime (RAGC). We propose that the spacetime manifold acts as an active, bandwidth-limited causal graph that drives the objective pruning of the quantum state space. Modelling spacetime as a Directed Acyclic Graph (DAG), we reconceive energy-momentum conservation as a strict local ledger balance condition at every actualization vertex. The paper makes three empirical predictions that are testable independently of the open mathematical derivations: (P1) the inferred value of H_0 should correlate with mean actualization density along the line of sight, explaining the Hubble Tension without dark energy; (P2) the vacuum energy contribution to the metric source term is structurally zero, not fine-tuned, with implications for CMB power spectra distinguishable from ΛCDM; and (P3) daughter spacetimes nucleated at causal severance boundaries inherit an effective cosmological constant determined by the local actualization flux at nucleation---a dynamical alternative to the anthropic landscape. Key mathematical results include: a spectral definition of the Actualization Projector (P_act) with a proof of vacuum energy suppression (the relevant theorem); and the Ledger Partition Theorem (the relevant theorem), establishing independent conservation across causal severances, which has been formally verified in Lean 4/Mathlib.% The RA Lean 4 proof files (RA_AQFT_Proofs_v10.lean and RA_Proofs_Lean4.lean) will be made publicly available on arXiv submission. The underlying Lean-QuantumInfo library (Meiburg, Lessa, and Soldati, 2025; arXiv:2510.08672) is publicly available at https://github.com/Timeroot/Lean-QuantumInfo. Furthermore, the framework categorically prohibits causally silent dark matter (WIMPs, axions, sterile neutrinos): a 100 GeV WIMP generates 10^25--10^38 times less actualization flux than equivalent baryonic matter, falling below the threshold for measurable gravitational lensing. Crucially, the observed phenomenology attributed to dark matter --- flat rotation curves, Bullet Cluster lensing offset, galaxy-galaxy lensing --- is accounted for without dark matter via the ∇^2λ mechanism and accumulated causal depth A_RA, classified across four distinct lensing regimes in the companion paper RADM. The conjectural mechanisms for flat galactic rotation curves and the Bullet Cluster offset---which follow from the same actualization-density field---are developed in the companion paper RADM. A new RA-native derivation of the causal set generative measure is presented: the Benincasa-Dowker sign criterion (S_BDG(v) > 0) as the discrete actualization filter yields a Poisson-CSG formula c_k^RA(x) e^-μμ^k with μ = λ V_coh p_th that is local and environment-dependent. A bandwidth-partition model predicts H_local ≈ 73.1 km s^-1 Mpc^-1 from the KBC void and a new falsifiable consequence: the Eridanus supervoid (δ ≈ -0.30) should give H ≈ 75.9 km s^-1 Mpc^-1. The Jacobson coefficient α = 2π is confirmed to within 2% when the full baryonic disk mass is used --- consistent with α = 2π exactly within the systematic uncertainty on v_flat and r_d. The generative measure (Derivation 1) is resolved by the O14 uniqueness theorem: the BDG integers are the unique growth rule with zero free parameters. The macroscopic limit (Derivation 2) is resolved by the BDG uniqueness chain (L01+O01+L11 Benincasa-Dowker Einstein-Hilbert). The field equation uniqueness (Derivation 4) is closed by the companion paper Relational Actualism: The Einstein Field Equations as the Unique Macroscopic Limit of the Actualization Graph (RACL), which proves G_μν = 8π G P_act[T_μν] with Λ = 0 as the unique consistent macroscopic description of the RA-CSG, using the Lean-verified LLC, the P_act conservation theorem, and Lovelock's uniqueness theorem. An alternative RA-native derivation via BDG uniqueness (L01+O01+L11 Benincasa-Dowker) arrives at the same result without Lovelock, using three Lean-verified inputs and one published theorem. The Einstein field equations are shown to be the unique consistent macroscopic description of the RA-CSG; and the speed of light is derived as the maximum causal bandwidth rate c = l_P/t_P, with E = γ mc^2 following from discrete counting alone.