The point I was trying to make is this. Stearic acid and coconut oil are the main acids. We know that you want a high stearic acid content for a good shave soap. However with only the order known you can have any amounts. I can have 80% stearic, 15% coconut and then the trace oils/fats. This would yield a great shave soap.You are right, we can not know exactly though the placement of a chemical in the ingredients list can give us a pretty good idea.
For example the Razorock P.160 ingredients list is:
Ingredients: Stearic Acid, Water(Eau), Cocos Nucifera (Coconut) Oil, Potassium, Hydroxide, Sodium Hydroxide, Tallow Acid, Hydrogenated Lanolin, Butyrospermum Parkii (Shea)Butter,Fragrance(Parfum), Argania Spinosa (Argan)Oil, Aloe Barbadensis Extract(Aloe).
From some soap recipes I've seen the saponification chemicals (Potassium (KOh) and Sodium Hydroxide (NaOh)) are often in total a small percentage of the fatty acids (Stearic Acid and Coconut Oil here). I've seen rations such as 1:7 to 1:6 in on-line recipes. Throw in the water and other ingredients and the total amount of saponification chemicals starts to approach just 10% of the total ingredients by weight. For example one possible hypothetical recipe per the above could be 60% Stearic Acid/Coconut Oil, 20% water, 5% each of the hydroxides and just 10% to cover all the other 6 ingredients or 1-2% each. Anything much larger and you wouldn't have the right fatty acid to Na/KOh ratio.
Given that this recipe is split between two saponification agents all the stuff that comes after such as tallow, lanolin and Shea Butter is likely at a low single digit percent of the ingredients total by weight for this soap. Hence why it's likely fair to refer to all the ingredients on this list that come after the sodium hydroxide as trace ingredients.
I can also have 50% stearic acid, 49% coconut oil and the rest trace ingredients and that would be less stellar shave soap. I still meet the ingredient list order. Please note that I only counted the acid percentages and not water not lye.
That was the point I was trying to make. We might be able to make some conclusions based on where water, lye etc are as well.