This paper investigates a reconfigurable intelligent surface (RIS)-assisted rate-splitting multiple access (RSMA) downlink with imperfect eavesdropper channel state information and finite-resolution RIS phases. The common stream carries public information, while user-specific private streams carry confidential information. For a conservative security assessment, each eavesdropper is allowed to remove the public stream and is given the other private streams as side information. We formulate a robust design of t he transmit precoders, isotropicartificial noise, common-rate allocations, and RIS phases that balances confidential and public throughput under rate and power constraints. Bounded errors in the direct and cascaded eavesdropper channels yield an effective-channel uncertainty bound valid across RIS phase updates. To address the resulting nonconvex problem, we construct conservative leakage bounds and convex inner transmit updates, initialize through a feasibility procedure, and search finite artificial-noise and RIS-phase candidates with explicit feasibility checks. For a fixed artificialnoise power and RIS configuration, the feasible inner iterates have a nondecreasing objective that converges in value, and their successive changes vanish. Accepted outer updates remain feasible and are finite in number. Our code is available at https://github.com/ABM-ADAM/RIS RSMA-secure.

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