Disproof of the conjecture.

I will disprove the Weaker Ifidonlike Conjecture. We fix 0-60 time as the performance measure.

[1] Engine #1: P(rpm) starts at 0, linearly moves up, and levels off at P1 @ R1, so that dP/dr(R1) = 0. We can certainly create such an engine. Assume that with an optimal transmission and shifting method (or CVT program), it achieves 0-60 of T1.

[2] Tranny #1, as a real-world tranny, will have a lowest ratio, be it CVT or not. There is therefore a threshold vehicle speed such that under this speed, if Engine #1 is run at R1, some mechanism (clutch or belt or viscous fluid with no lock) will be slipping.

[3] By laws of elementary physics, if a mechanism (here the tranny) can be used to transfer force/power in two states, a locked state or a slipping state, there is a definite, discrete drop in its efficiency in the slipping state, due to frictional loss.

[4] I claim the existence of an rpm R1e
[5] In summary, what we've proved so far is for Car #1, the optimal tranny/shifting strategy always involves locking the tranny at some rpm R1e prior to R1. You may want to start off by slipping the clutch, but in the end you'll always have the engine rpm dip, even if ever-so-slightly. Let's remember that this strategy gives the optimal 0-60 time of T1.

[6] Now construct an Engine #2: P(rpm) is still maxxed out at P1 @ R1, but is higher than Engine #1's before R1. Especially at R1e, Engine #2 makes more power.

[7] Now couple Engine #2 with the same Tranny #1 and use it in Car #2. Already, the same shifting strategy will yield a smaller 0-60 time T2e
[8] Now construct an Engine #3, where P(rpm) is everywhere a fraction 100%-x% of P(rpm) of Engine #2, x being small. Couple this engine with the same Tranny #1 in Car #3. Under the same shifting strategy, the performance T3x is a continuous function of x. So there must be a positive x, so that T3x
[9] This Engine #3 has peak hp P3=P1*(100%-x%)
Note that since this is a mathematical proof, I'm forced to use small number epsilon-delta type of arguments. But in real world situations, the optimal clutch engagement rpm R1e likely happens a lot sooner than R1 (check out some cars like M3 with launch control). Then you can find a bigger x% as well.

What does this mean? It means you can't give a blanket statement that "a 244 peak-hp engine will always outperform a 243.9 peak-hp engine with the right tranny". Likewise, you probably can't say it for 244 vs 240. At which point can you make a blanket statement, if ever? Are you sure? If you only know a single hp number at a lofty rpm, how do you know what happens before this rpm?

Conclusion: Even with a choice of tranny, it's the entire hp curve that matters, not the peak number.