User blog comment:B1mb0w/Strong D Function Calculations/@comment-5529393-20150805103642/@comment-5529393-20150806045433

No, the logic does not flow correctly. You may well have established the initial conditions for D(1,0,n), D(2,0,n) D(3,0,n) and $$\phi = \omega, \omega+1, \omega+2$$ respectively. From there, a theorem that assumes the statement for l-1 and $$\phi$$ and proves it for l and \phi+1 will, by standard induction, will establish the statement for all D(m+1,0,n) and $$\phi = \omega + m$$. That is all that is proven, and so far it agrees roughy with the results of Hyp Cos and myself.

Where you go wrong is rule L1, where, solely on the basis that $$D(l-1,0,1) = f_\phi(3)$$ (that = still doesn't work but never mind for now) you claim this proves that $$D(l,0,1) >> f_{\phi+1}(3)$$. This is not proven at all, since your previous calculations were based on the statement $$D(l-1,0,n) = f_\phi^{n-1}(f_\phi(3))$$ where n can be anything.