This lets us understand that if we add one dash of 75% bitters to the one cocktail and two dashes of 37.5% bitters to another cocktail, the amount of aromatic and flavorful molecules we are contributing to each cocktail is the same
No. It's not. They both have their own flavour profile. Which takes me to my last point on this subject...
You have had plenty of opportunities in this discussion to assert that the dilution to bottle proof causes a chemical reaction such as louching, filterable precipitation, etc. that permanently changes the chemistry of the bitters. And several other people have suggested that this might be the case. Since you have not made such a claim, your entire argument is predicated on the supposition that the dilution to bottle proof changes the flavor profile in a permanent and characteristic way that endures through further massive dilutions into other liquids simply by virtue of having been diluted in the bottle
I hope you understand that flavor and aroma perceptions are created through the sensation of certain molecules at certain concentrations. And I hope you understand that if, for example, 83 parts per million of quinine produces a certain taste sensation, it doesn't matter how the quinine molecules got to have a concentration of 83 parts per million. A simple water and quinine solution that started out at 83 ppm will taste exactly the same as one that started out at 166 ppm and was diluted down to 83 ppm. The reason they taste the same is because the chemistry is the same.
When we make a bitters infusion we have created a solution containing water and ethanol and the various flavorful and aromatic molecules that resulted from the infusion. In this context, the water and ethanol are effectively flavorless/odorless and what we care about are the flavorful and aromatic molecules. If there is no chemical reaction or other effect of dilution such as louching, precipitation, etc., then the ratio of these flavorful and aromatic molecules will not change with respect to each other no matter how much the solution may be diluted. For example, if the original solution has 100 mg/l of Molecule A and 50 mg/l of Molecule B (a 2:1 ratio) and is then diluted by 100%, the new solution will have 50 mg/l of Molecule A and 25 mg/l of Molecule B (also a 2:1 ratio). We can dilute this solution as much as we want, and the ratio of Molecules A and B will always be 2:1 unless something causes one of them to drop out of solution.
If we were to do a chemical analysis of your 75% bitters to look at the aromatic and flavorful molecules, we could see that it has, say, 100 mg/l of Molecule A and 50 mg/l of Molecule B and 20 mg/l of Molecule C and so on. When we make a 100% dilution, so long as this reduction in abv doesn't cause any of the aromatic and flavorful molecules to come out of solution, the 37.5% solution now has 50 mg/l of Molecule A and 25 mg/l of Molecule B and 10 mg/l of Molecule C and so on.
So, let's say that one dash = 1 milliliter. 1 ml of the 75% solution will contain 0.1 mg of Molecule A and 0.05 mg of Molecule B and 0.02 mg of Molecule C and so on. 1 ml of the 37.5% solution will contain half as many of each flavorful and aromatic molecule: 0.05 mg of Molecule A and 0.025 mg of Molecule B and 0.010 mg of Molecule C and so on. This is not fundamentally different from the dilution of ethanol with water (except that when we dilute ethanol we tend to express the amount of ethanol in terms of volume rather than mass).
So now we're putting dashes of these solutions into a cocktail. If we use one milliliter of the 75% solution, we are dosing the drink with 0.1 mg of Molecule A and 0.05 mg of Molecule B and 0.02 mg of Molecule C and so on. If we use two milliliters
of the 37.5% solution, we are also
dosing the drink with 0.1 mg of Molecule A and 0.05 mg of Molecule B and 0.02 mg of Molecule C and so on, because we used twice as much solution. This means that the same amount of aromatic and flavorful molecules will be present in both drinks
, and the only chemical difference between the two cocktails will be that the one dosed with the 37.5% solution will contain an additional 1 ml of water.
This is basic chemistry and mathematics. If you don't understand this or willfully persist in insisting that it isn't so, I don't think there is any basis for those who do understand these things to continue this conversation with you. All I can suggest is that you refer this question to a chemist. I should hasten to add that there are any number of possible explanations for your observations that would be entirely valid. For example, if you are not making your comparisons in a properly controlled way there is the huge issue of confirmation bias. On the chemistry side, as several of us have suggested, there could be chemical changes that result from the reduction in abv (most likely certain molecules precipitating out of solution). This seems like a fairly likely explanation. I haven't even said that what you claim to observe doesn't happen. I and others here have mostly taken exception with the reasons you have given to explain your observations, because those explanations simply don't hold up according to really very basic scientific principles.