An ideal gain contract multiplies the loaded node, not the open source voltage. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The gain stage receives the loaded node

The source is 6 volts, but the input node is only 3 volts after loading.

Vin=3 VV_{\text{in}} = 3\ \text{V}
Loaded node before gainThe gain input is the loaded node.6 V1 ohm1 ohmA3 A3 A+-3 V+-3 Voutputload

The ideal gain multiplies the loaded node

The declared gain of 2 acts on the loaded input, giving 6 volts.

Vout=23 V=6 VV_{\text{out}} = 2\cdot 3\ \text{V} = 6\ \text{V}
Loaded gainThe gain contract uses the loaded input.V3 VV6 V+-3 V+-6 Vgain