A Deterministic Framework for Stability and Transitions via Curvature Thresholds and the Konkle Unified Baryonic Equation (KUBE)

Baryonic Matter Physics: A Deterministic Framework for Stability and Transitions via Curvature Thresholds and the Konkle Unified Baryonic Equation (KUBE)This white paper presents a deterministic framework describing how matter maintains stability and undergoes structural transitions when geometric curvature and compression exceed intrinsic accommodation limits. Rather than relying on multiple independent force thresholds, the framework proposes that baryonic matter systems remain stable while their internal curvature and compression remain within the phase-coherent accommodation capacity of their constituent carriers. When this capacity is exceeded, a deterministic transition occurs at what is termed a Snap Point.Snap Point transitions represent structural reorganizations of matter and energy that may manifest as binding events, gravitational collapse, particle emission, phase transitions, or boundary-driven attraction depending on the physical regime involved. The framework therefore proposes a unifying geometric principle underlying phenomena that traditionally appear unrelated across nuclear, atomic, gravitational, and vacuum-boundary systems.Central to the model is the Konkle Unified Baryonic Equation (KUBE)f = mc² / hwhich links rest mass to an intrinsic oscillatory coherence frequency. This formulation implies that matter possesses a persistent oscillatory reservoir that exists even at absolute zero. The intrinsic oscillatory coherence associated with mass defines the fundamental capacity of matter to accommodate curvature and compression before structural transition occurs.Within this framework, stability is interpreted as a condition in which imposed geometric curvature remains within the accommodation capacity determined by the mass-associated oscillatory coherence. When external compression, gravitational curvature, electromagnetic confinement, or boundary constraints exceed this capacity, the system crosses a deterministic threshold and reorganizes into a new configuration.The paper develops a dimensionless curvature-threshold parameter that compares imposed curvature loading with the intrinsic accommodation capacity of the system. When the parameter exceeds unity, a Snap Point transition occurs. This concept is applied across multiple physical regimes including nuclear structure, neutron star stability, black hole collapse conditions, and vacuum boundary phenomena such as the Casimir effect.The framework therefore proposes a unified geometric interpretation of stability and transition behavior across scales ranging from quantum systems to astrophysical structures. Rather than viewing nuclear, gravitational, and vacuum phenomena as governed by unrelated mechanisms, the deterministic curvature-threshold approach suggests that many observed transitions may arise from the same underlying geometric accommodation principle.