Yes, and for the first reason I've often specified that it's a fully acting/freely acting throttle that's not allowed. In fact in my second reply to you on this link I posted "free acting" to make it clear.
Technically the second two of your statements is incomplete for compliance with the law. Remember the power is supposed to phase down as the road speed approaches the legal limit. The problem with your supposition is "phase down from what?", since prior to that you are varying the power. I'm sure you can see that problem, it's akin to when people use two comparatives like "more better". (Than what?)
However that is "legalese", in practice many manufacturers ignore the requirement for power phase down so you can ignore it too.
The Japanese who were early into pedelecs did draft very accurate law regarding phase down and the details are in this extract of an article I've published elsewhere. It's a nightmare we wouldn't want here!
The explanation for the very early phase down is more complex, and it results from Japanese law on electric assist pedal cycles. The Japanese have determined that the maximum power allowable must not exceed the power the rider puts in (1 to 1), and that this should only be fully available within normal cycling speeds. Unfortunately for us, the Japanese have a very different view on cycling speeds to that of UK riders, They regard their common cycling speed as being 15 kph (9.4 mph), and for "sports" riders like our lycra brigade, 24 kph (15 mph), which would raise a laugh from UK club riders who can often average 20 mph for an hour in moderately hilly areas. Since sports riders don't use electric assist bikes, only the "common" bike's speed is legislated for. Therefore in accordance with that, the Panasonic design has integral to it the phase down above full assist at 15 kph (9.4 mph) when the bike is in top gear.
But that's not the end of it, for Japanese law prescribes the power phase down slope as well. Since an analogue slope doesn't readily match digital electronic systems working, Panasonic have chosen to have four step downs giving a rough tail off of power corresponding with the legal requirement, which is expressed in Japanese law by this equation:
1 - ( [kph - 15] / 9 ) = assist factor
where kph is the road speed.
Quite simply what this means is the road speed in kph, minus 15 (the 1 to 1 power assist limit), then divided by 9 produces a result which is subtracted from 1.
In a practical example, at 20 kph (12.5 mph), taking 15 from that 20 kph gives us 5. Then that 5 divided by 9 gives 0.55 recurring. To complete the equation we take that 0.55 from 1 to give 0.45 or 45%, and that's the ratio of rider power that the motor is allowed to assist with at 12.5 mph.
At the lower speed of 11 mph (17.6 kph) using the same calculation, 17.6 minus 15 then divided by 9 and taken away from 1 gives 0.71 or 71% of the riders input given as motor assistance. At the higher speed of 13 mph (20.8 kph), only 36% of rider input is given by the motor.
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