κ-Theory: History-Dependent Gravity and Nonlinear Structure Formation

κ-Theory: History-Dependent Gravitational Dynamics — Description This work introduces κ-theory, a nonlinear extension to gravitational collapse in which the evolution of matter depends not only on local energy density but also on the spatial structure of that density. Specifically, κ-theory incorporates a gradient-dependent correction term that amplifies collapse behavior in regions of high structural intensity while remaining negligible in uniform systems. The central result is that gravitational collapse becomes structure-sensitive rather than purely state-dependent. Under fixed parameters, the model produces a continuous scaling of black hole seed masses as a function of density-gradient intensity, generating seeds in the range of 105–108M⊙10^5–10^8 M_105–108M⊙ without parameter tuning. This directly addresses the longstanding problem of early supermassive black hole formation by shifting the focus from growth-rate limitations to initial seed conditions. The framework is tested through controlled simulations and compared against observed constraints from high-redshift quasars and ultramassive black holes such as TON 618. Results show that κ-theory is consistent with the required seed-mass regime and compatible with observed large-scale endpoints, while preserving standard gravitational behavior in low-gradient environments. Importantly, κ-theory does not introduce time reversal or stored historical states. Instead, it implies that physical systems are path-sensitive but causally consistent: the universe does not retain the past as an accessible state but expresses it through present structural configuration. The model is fully falsifiable. It fails if seed-mass scaling does not emerge under fixed parameters, if collapse behavior does not correlate with density gradients, or if the correction disrupts uniform-field gravitational predictions. κ-theory is therefore presented as a testable, internally consistent candidate modification to gravitational dynamics, capable of reproducing key features of observed structure formation while remaining compatible with existing physical constraints. It is not claimed as empirically confirmed, but as a model that survives all current logical and numerical tests and invites direct observational and computational validation.