Space as an Emergent Property of Matter: The Box A Hypothesis

Context. The standard cosmological model requires two undetected components — dark matter and dark energy —to account for observed galaxy dynamics and cosmic expansion. Modified gravity theories such as MOND reproducegalactic rotation curves without dark matter but lack a cosmological framework and require an empirically postulatedacceleration scale a0.Aims. We develop Box A, a scalar field theory in which space emerges from matter at the speed of light c, and testwhether a single field equation can simultaneously account for Newtonian gravity, MOND-like dynamics at galacticscales, and cosmic expansion without free parameters.Methods. The governing equation □A = (8πG/c2)ρA + λ2(1 − A) with g = −c2∇(lnA) and λ = H0/c is solvedanalytically in the cosmological and weak-field limits. Predictions are compared against four independent datasets:cosmic chronometers (Moresco et al. 2016, 2022), SPARC rotation curves (Lelli et al. 2016), KiDS-1000 weak lensingRAR (Brouwer et al. 2021), and the Bullet Cluster convergence profile (Clowe et al. 2006).Results. The field exponent α = 1.137 and present-day value A0 = 0.5 follow analytically from the field equation withΩm as the sole input. Box A achieves χ2/N = 2.83 on SPARC rotation curves versus MOND’s 7.67, and performs 11×better than MOND on KiDS-1000 weak lensing data with the theoretically derived a0. The Bullet Cluster convergenceprofile is reproduced geometrically without dark matter (χ2/N = 6.2 versus 44.6 for GR+NFW).Conclusions. Five parameter-free predictions follow from the field equation alone: α = 1.137, A0 = 0.5, a0 ∼ cH0,γ =3/(2α), and cGW = cEM. The MOND transition radius is predicted to migrate outward with cosmic time as H(t)decreases, consistent with Genzel et al. (2017). Open tensions remain in the Pantheon+ supernova sector (∆χ2 ≈ +10versus ΛCDM) and for isolated dwarf satellites in dominant external fields.