The core1 is able to reach R1 and R2 connected interface and loopback0 interfaces. The problem is that R1 cannot reach R2's loopback and vice versa. Each device is able to hit each others physical interfaces.
R1 - loopback0 10.x.x.1/32
Router EIGRP 1
network 10.x.x.1 0.0.0.0
network 10.x.x.2 0.0.0.0
network 10.x.x.3 0.0.0.0
eigrp router-id 10.x.x.1
no auto-summary
R2 - loopback0 10.x.x.2/32
Router EIGRP 1
network 10.x.x.1 0.0.0.0
network 10.x.x.2 0.0.0.0
network 10.x.x.3 0.0.0.0
eigrp router-id 10.x.x.2
no auto-summary
Core1 - loopback0 10.x.x.3/32
Router EIGRP 1
network 10.x.x.1 0.0.0.0
network 10.x.x.2 0.0.0.0
network 10.x.x.3 0.0.0.0
eigrp stub connected summary
eigrp router-id 10.x.x.3
no auto-summary
It seems to me that Core1 is not passing its knowledge of R1 and R2's loopbacks.