The major problem with this this is that not all schools within the same style teach katas in the same order. For example, Kobayashi Shorin-ryu teaches the Naihanchi series before the Pinan series (as Chosin Chibana did), whereas that's not the case in other Shorin-ryu lineages.
Like I said, I am looking at this a little differently.... Your example above, supports what I was trying to say. The first form / kata that a student learns, contains the foundation upon which the whole art is built. Kobayashi Shorin-ryu starts with a different kata than the rest of Shorin-ryu.... because they find the foundation of that other kata, to be more in line with the way that they see Shorin-ryu. If Kobayashi Shorin-ryu did everything exactly the same as all the other Shorin-ryu schools.... they would not need to use the term "Kobayashi."
A lot of people think that the kata / forms are a dictionary of moves that an art contains. If you can't find a technique in that art's kata, that art does not do that technique..... The problem with kata = dictionary of techniques theory is that you end up with the following dictionary: apple, boy, apple, boy, apple, boy, boy, boy, apple, boy, apple, boy, apple, boy, boy, boy, apple, boy, apple, boy. Then we get people saying, thats dumb.... it should just be: apple, boy.... and you cannot use carrot, ever, otherwise you are not doing the art.
Gichin Funakoshi himself stated that (in the case of Shuri-te styles) that if a student knows the whole Heian (Pinan) series, he already has a complete working system. Notice, he didn't say Heian Shodan only; he said the whole series (e.g., you don't even kick in Heian Shodan/Pinan Nidan).
The question was about a summary..... Taikyoku Shodan has a summary of all the principles, strategies and the core foundation of Shotokan. Are you saying that Funakoshi's complete system (Heian series) could not do a kick? Because you can not find it in one of the kata?
This shows a little of my disappointment with a lot of the Japanese martial arts that we study..... We study them like they are a collection line dances, that define all the techniques that are accepted as part of the art. One group teaches in one order, another group in a different order.... but no one knows why. How dare you learn that kata at orange belt??? We don't teach that until black belt!!! Why? Who knows????
No one stops and thinks about why did the founder select those techniques, those kata and why were they taught in that order. There is more to it than just random moves in a pattern. Too many people have been adding kata, removing kata and changing the order that they are taught in... without knowing what the kata is teaching.... but, but, but they memorized the moves and the order and everything.... We do that technique in front stance, not back stance.... Okay, but what does that change? Its just how we do it....
Instead, we need to look at the kata as grammar books, not dictionaries. They are for teaching you how to use the words, how to put them in combination how to use them to say what you want to say. No one looks at your elementary school grammar book to define what words you can and cannot use, based on what words happen to be in the grammar book. The hope is that you expand your vocabulary beyond the few words used in the book. If you learned the lessons in the book right, then you can use all the words there are, effectively in your communication. This is how the kata were intended to be used.
The kata you learn first, is the foundation of the art. It contains the core principles of the art. As you learn more of the art, you will be going deeper into those principles and ideas.... but the summary of the core principles and ideas are in that first kata. Ideally, you should take the things you learn in your first kata, and find them in your next kata.... then find how the next kata expands on the same ideas... So, kicks are not introduced in the first few kata.... what principles and ideas are? How are those principles and ideas expanded upon? How are kicks introduced to those principles and ideas? This will show you how to improve your kicks, by utilizing the core fundamentals of your art. Just because you don't find a specific technique in your set of kata, does not mean that you can't do it.... it means you need (and should) do the work to find how to apply the principles and ideas of your art, to apply that technique. It will make this technique much more effective for you.... as it will be part of your personal system.
If you want the dictionary.... just take every unique technique for you set of katas, and do each technique once... memorize the order.... play some music in the back and do it to the beat....