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In the upcoming sixth generation (6G) of wireless communication systems, reconfigurable intelligent surfaces~(RISs) are regarded as one of the promising technological enablers, which can provide programmable signal propagation. Therefore, simultaneous radio localization and mapping(SLAM) with RISs appears as an emerging research direction within the 6G ecosystem. In this paper, we propose a novel framework of RIS-enabled radio SLAM for wireless operation without the intervention of access points (APs). We first design the RIS phase profiles leveraging prior information for the user equipment~(UE), such that they uniformly illuminate the angular sector where the UE is probabilistically located. Second, we modify the marginal Poisson multi-Bernoulli SLAM filter and estimate the UE state and landmarks, which enables efficient mapping of the radio propagation environment. Third, we derive the theoretical Cramér-Rao lower bounds on the estimators for the channel parameters and the UE state. We finally evaluate the performance of the proposed method under scenarios with a limited number of transmissions, taking into account the channel coherence time. Our results demonstrate that the RIS enables solving the radio SLAM problem with zero APs, and that the consideration of the Doppler shift contributes to improving the UE speed estimates.