Jacob's ladders and the first asymptotic formula for the expression of the sixth order $\mathrm{\mid }\zeta (1\mathrm{/}2+i\phi (t)\mathrm{/}2){\mathrm{\mid }}^4\mathrm{\mid }\zeta (1\mathrm{/}2+it){\mathrm{\mid }}^2$

t is proved in this paper that there is a fine correlation between the values of $\mathrm{\mid }\zeta (1\mathrm{/}2+i\phi (t)\mathrm{/}2){\mathrm{\mid }}^4$ and $\mathrm{\mid }\zeta (1\mathrm{/}2+it){\mathrm{\mid }}^2$ which correspond to two segments with gigantic distance each from other. This new asymptotic formula cannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.