KoR Part III introduces the concept of the Refusal Constant (R) - an operator that renders refusal not as contingent behavior, but as a principle of resilient cognition. Where Part I defined refusal-first as an architectural stance, and Part II mapped refusal into a field model of cognition, Part III demonstrates that R persists across modalities, agents, and contexts as a measurable constant anchoring ethical dynamics. This paper provides both symbolic and empirical evidence for R. In this framing, refusal is not mere negation but a generative act: it logs traces, shapes trajectories, and stabilizes cognition under pressure. Part III formalize R as a constant - ethical, structural, and computationally demonstrable. In doing so, it reframes refusal from an obstacle to progress into the very principle that allows resilience, accountability, and co-psychogenetic emergence. KeywordsArtificial Intelligence, AI Ethics, Refusal-First, Kernel of Resilience, Refusal Constant, Cognitive Architecture, Ethical AI, Differential States, Traceur Role, Accountability, Symbolic Cognition, Cryptographic Proofs, Governance.