We prove by exhaustive algebraic enumeration that cell proliferation governed by three simultaneous structural conditions — nearest-neighbor coupling (contact inhibition), binary proliferation gating (p53/RB), and second-order metabolic memory (mTOR/telomerase) — admits exactly one stable growth mode. Breaking any single condition produces exponential growth. Restoring any single condition in isolation either accelerates tumor growth or arrests tissue renewal entirely; only simultaneous restoration of all three returns the system to governed growth. All seven Hanahan-Weinberg cancer hallmarks map onto disruption of these three conditions (7→3→1 compression). The framework generates a specific, falsifiable prediction: triple-combination therapy (CDK4/6 inhibitor + mTOR inhibitor + YAP inhibitor) should produce a discontinuous phase transition in tumor growth kinetics, observable in standard cell culture. Independent confirmation is provided by the naked mole-rat, whose cancer immunity derives from redundant coupling gates rather than enhanced repair or immune surveillance.