Yeah I think you're on to it. The more factors a product has the more (x+n) squares does it have.
The only constants we have for all our (x+n)^2 squares are d and f. Everything else depends on the different records.
But then if h is a variable, what is it connected to? We have h-families. Is then h related to the number of factors a product has? For a semiprime, we have 2 families? I remember the >>5690
>Using an arbitrary divisor for f, then each of the eight triangles will have one OR one of two (the latter when c is large and the product of two different prime numbers) configurations in each triangle.
Although I don't think we ever figured out how polite numbers are related to the triangles, did we? Nor do I think we ever actually "got" the configuration of the triangles correctly either.