Eventual existence of central-anchor certificates

For every real $c>C_0$, there exists an integer $R\ge201$ such that every sufficiently large natural $n$ admits a central-anchor certificate. More explicitly, it gives a valid large-prime cofactor choice $q$, its full anchor set $A\subset(n,2n]$, and central divisor $D$, with

where $T_c(n)$ is the central tail product. Every prime divisor of $D$ is at most $2R+1$, and for every prime $p\le2R+1$,

The certificate packages the exact central product together with a positive tail-valuation reserve.