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On the nonzero stationary branch of five-mode magnetoconvection, put $s=a^2$ and $m=(4-\varpi ){\zeta }^2/\varpi >0$. The temperature equations first give $b=a/(1+s)$ and $c=s/(1+s)$. The magnetic equations then giveDivide the steady first equation by $\sigma a$ and substitute these expressions. The exact branch isExpanding at $s=0$ givesNear $\varpi =2$ the required amplitude restriction $a^2\ll {\zeta }^2$ ensures $s\ll m$. For $\varpi \le 2$, $r_2>0$, so the paired equilibrium points emerge in the forward direction $r>1+q$. For fixed $q>0$ and small $\zeta$, the pitchfork reversal near geometric ratio two in magnetoconvection occurs atThis follows by expanding the exact zero-slope equation $q\varpi (2-\varpi )+(4-\varpi ){\zeta }^2(1+q)=0$. Above this value the branch initially runs backwards into $r<1+q$; at $q=0$ there is no reversal. This is a degenerate pitchfork bifurcation at $r_2=0$, not a conclusion that every emerging state is stable. If $B_s>0$, the center-direction cubic term has the opposite sign to $r_2$: the forward branch is locally attracting and the backward branch repelling. If $B_s<0$, an unstable transverse mode remains.

For the nearby geometry, the next coefficient is $r_4=q[(2\varpi -5)/m^2+(2-\varpi )/m]$, which is negative near the reversal. Thus a small positive $r_2$ produces a nearby maximum of $r$ at $s\simeq -r_2/(2r_4)>0$; this fold approaches the pitchfork as $r_2\downarrow 0$. Once $r_2<0$ the small-amplitude branch is backward. The exact formula eventually grows like $r\sim s$, so a backward branch must turn at a finite amplitude, potentially outside the small-amplitude expansion.