Simplest case of Kahn System causing phase modulation of main carrier. That makes it most like the Magnavox system, which phase modulates the main carrier with L-R within one Radian.
Carrier frequency 1000 kHz, 1000 watts. Vector magnitude 1.
Audio sideband for 1000 Hz at 1001 kHz, 250 watts. Vector magnitude 0.5. 100% modulation for this channel.
An audio vector spins clockwise which is one half the magnitude of the carrier. At the beginning of the full cycle, the magnitude is 1.5, the carrier phase shift is zero. At half cycle, the magnitude is 0.5, the carrier phase shift is also zero. At one quarter cycle, the magnitude is SQRT (1.25), the phase shift is Arctangent (0.5)= 26.6 degrees. At three-quarter cycle, the magnitude is SQRT (1.25), the phase shift is Minus Arctangent (0.5)=Minus 26.6 degrees. Since one radian is approximately 57.3 degrees, Kahn would seem to be very similar to Magnavox without the pilot frequency, with a slight difference in the magnitude of phase modulation.
This would be detected as 1000 Hz in one channel, no audio in the other channel.
Next simple case.
Carrier frequency 1000 kHz, 1000 watts. Vector magnitude 1.
Audio sideband for one sideband for 1000 Hz at 1001 kHz, 250 watts. Vector magnitude 0.5.
Audio sideband for other sideband for 1000 Hz at 999 kHz, 250 watts. Vector magnitude 0.5.
Audio vectors spin in opposite directions, one CW, one CCW. The perpendicular vector phase shift cancels at each point in the cycle, resulting in zero phase shift at each point in the cycle.
Vector magnitude at beginning of cycle, 2.
Vector magnitude at 1/4 cycle, 1.
Vector magnitude at 1/2 cycle, 0.
Vector magnitude at 3/4 cycle, 1
Audio vector is identical to 100% AM modulation at 1 kHz, and is in both channels equally.