  The Recurrence Axiom for a class $\mathcal{P}$ of \pos\ and a set $A$ of
parameters is an axiom scheme in the language of ZFC asserting that if a
statement with parameters from $A$ is forced by a poset in $\mathcal{P}$, then
there is a ground containing the parameters and satisfying the statement.
  The tightly super-$C^{(\infty)}$-$\mathcal{P}$-Laver generic hyperhuge
continuum implies the Recurrence Axiom for $\mathcal{P}$ and
$\mathcal{H}(2^{\aleph_0})$. The consistency strength of this assumption can be
decided thanks to our main theorems asserting that the minimal ground (bedrock)
exists under a tightly $\mathcal{P}$-generic hyperhuge cardinal $\kappa$, and
that $\kappa$ in the bedrock is genuinely hyperhuge, or even super
$C^{(\infty)}$ hyperhuge if $\kappa$ is a tightly
super-$C^{(\infty)}$-$\mathcal{P}$-Laver generic hyperhuge definable cardinal.
  The Laver Generic Maximum (LGM), one of the strongest combinations of axioms
in our context, integrates practically all known set-theoretic principles and
axioms in itself, either as its consequences or as theorems holding in (many)
grounds of the universe. For example, double plus version of Martin's Maximum
is a consequence of LGM while Cicho\'n's Maximum is a phenomenon in many
grounds of the universe under LGM.
