The shape of the fade does not decide what the middle sounds like.

A crossfade takes one source down while it brings another up, and the only thing that matters is what the two sum to in the middle. That is not decided by the curves. If the two sides are the same signal — a punch-in, a loop point, room tone joined to itself — their amplitudes add. If they are unrelated — two takes, two rooms, dialogue against music — their powers add. The fade dialog does not ask which you have, and it is the only thing that decides the answer.

The engine is free and needs no account. A linear fade is exactly flat on the same take and −3.01 dB in the middle on two different sources: a hole. An equal-power fade is exactly flat on two different sources and +3.01 dB on the same take: a bump. Each law is wrong by the same amount for the material the other one is right for, and no law is right for both — so an editor with one default and a timeline with both kinds of join is choosing which joins to get wrong. The one useful consequence: the −4.5 dB law most editors ship is exactly flat at a correlation of √2 − 1 = 0.414, which is about what two microphones on one source in one room are. It is not a hedge; it is the right law for the case in the middle. Every lane ships a worked example that costs nothing. Writing the report needs credits.