Productive values are values that let you sustain your life in it's biological requirements and it's requirements for happiness. (E.g. working as a programmer helps satisfy your need for food/shelter/medicine and also allows you to satisfy your passion for a life worth living in programming ). Ayn Rand shows that the requirements to man's life are objective [external to conscious desire]. There is no subjectivity in your bodies needs for energy (via need for food), there is no subjectivity in the use of reason to accomplish values, and that there is no subjectivity in the requirements for how you reach happiness by the use of your individual judgement to fulfill your life.
Productive actions come in many concretes, but all individuals are unified in that they are actions that satisfy the objective requirements of how individual maximally live.
If productivity were truly subjective, anything could keep us alive and happy. But you cannot eat off playing video games [at least not if you aren't a twitch star ;)], and you cannot find happiness by doing a career you hate.
What is it "to live"? Even more of a mystery is what is it to "maximally live"? You are reducing all of life to a single dimension that you haven't even defined. There may be an objective minimum amount of calories that are necessary to stay alive/awake but I don't think that raw survival is super relevant here; what value is there in intaking a single one beyond that? The things that make us happy at one point in our lives aren't necessarily always going to make us happy, in fact our ideas of what it is to be happy can easily fluctuate throughout our lives, and definitely do fluctuate from person to person. There's very little in this world that is as cut and dry as you seem to imply.
No honest philosophy claims to supplant the special sciences, only serve as a foundation, nor will it tell you exactly what you must do to apply those principles to your life. If rigid dogma is what you expect or seek, I suggest investigating religion instead.
I really don't think I am, I'm trying to tell you that you keep referencing subjective values as if they can be assessed objectively. An example from the comment above is the following subjective value implied as an objective value: a long life is a better life than a not long life. I know it may sound preposterous but for every scenario we could imagine there is always a way to look at an action as a good thing or a bad thing depending on your perspective, even chugging rat poison. Perhaps the results of my death from poisoning is that someone else is able to survive due to the whatever circumstances surround the scenario; in this case I may be balancing the value of my own continued existence against that of someone else's and you want to tell me you there's a framework that is somehow going to guide me into making an objectively correct choice about who lives and dies?
> Objectivism deductively and inductively proves that certain actions are an objective good for the soul as a condition of being human
I disagree with this wholeheartedly.
I have seen zero proof of this and I really don't think it can be proved because the objective universe does not track goodness in any way, it is a concept defined entirely within our minds and does not have an objective physical reference we can test or compare against.