I’m going to say the controversial thing… But what you want doesn’t exist in the film world. There is no ‘true correct way’ to invert a type of film.
In the old days the result would also be affected by the method of correcting the color balance and the type of paper it was printed on.
The ‘inversion’ has a lot of effect on the result, and no difference in the digital world.
This is also were the difference between different scanning labs come in. One just uses a preset and calls it done without judging the output, the other is doing half of a photo edit to give you a result.
A lot of the result is determined by artistic choices during the inversion and editing. A good proper lab will create profiles for its customers so they know what your tastes are and your expected result,so they will work towards that.
As far as i know - but I’m no expert at all!! - most c41 inversion software still needs to set a blackpoint and whitepoint. They try to determine this or you could set it yourself, but basically these vales need to be chosen during inversion. Blackpoint can be picked from unexposed piece of film, but you might set it higher for more contrast, or if you overexposed or if you want a different colorcast in your shadows.
Same for the whitepoint, but this can only be guessed or picked manually.
What makes the difference between the filmstock is how the color and exposure is distributed between those points.
Imagine a film has been made for a certain type of sensitivity for reds around the exposure sensitivity for caucasian skin. But what happens to the the reds around that exposure point? Do they become shadows gradually or abruptly (contrast), do they keep saturation or loose it (or gain it), etc… This is what makes the films differently.
But imagine two people shoot the same film stock (down to even the same batch number of modern Porta 400 135 for example).
Those two people use different developments of their film, use a different scanner with different exposure settings (or a different DSLR with different lightsource and different lens). No way any software could do ‘the one perfect inversion’ for this film. There are way too many variables… And way more astistic choices to make.
That’s why you scan your film yourself. The inversion is already 50% of your image edit, and I want to do it myself (or the professionals I would trust to do this are to expensive for my hobby :)).
And don’t forget, most films with the same name have huge differences. The portra 400 135 is different to the 120… It’s different to the one sold 15 years ago. It might be different between the US and Europe… It might be fresh or it might be stored in the sun. It might be expired. It might have been in a camera for a year, or it might have been shot and developed on the same day…
There is no ‘correct’ way for a film to look. That’s not how film works (even though people are let to believe it).