User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-24509095-20140509071457/@comment-5150073-20140605095213

By the way, $$\chi$$ function, in its full power, must be binary. Can we turn it into unary function with catching up the binary variant at $$\chi(\varepsilon_{M+1})$$, like it has been done for $$\vartheta$$ and $$\psi$$?