Collaborative perception (CP) extends sensing range through feature sharing, but most systems remain LiDAR-centric. Camera and 4D radar sensing combines dense semantics with lower-cost range--velocity measurements, yet exploiting their complementarity across agents remains difficult. Camera depth ambiguity produces spatially diffuse BEV evidence, while sparse transmission couples the choice of evidence to its subsequent contribution. Separate acquisition and aggregation objectives can assign conflicting source preferences to the retained evidence. We propose RC-GeoCP, connecting radar-grounded representation with persistent receiver--source attribution. Geometric Structure Rectification (GSR) uses radar-conditioned deformable sampling and gated calibration to construct grounded BEV features before communication. On these features, Uncertainty-Aware Communication (UAC) combines receiver demand with semantic confidence and radar support in a pre-delivery responsibility field that selects sparse support within fixed quotas. The Consensus-Driven Assembler (CDA) maps the same field into a bounded source mixture, carrying acquisition preferences into assembly. Persistent attribution coordinates spatial selection and source weighting across sparse transmission. Across two datasets and three aggregation backbones, RC-GeoCP consistently improves detection. Its sparse model retains 98.6%/96.6% of dense [email protected] at 10.88/4.95 MB per link. Code will be released.

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