Harmonic chainlet characterization

Let $A$ be a chainlet of class $N^r$, and let $Ch$ map differential forms of class $B^r$ to chainlets. A form is harmonic when it satisfies the relevant harmonic equation, and a chainlet is harmonic when it satisfies the corresponding chainlet equation. Harmonic chainlet characterization. $A$ is harmonic if and only if

$$A=Ch(\omega)$$

for some harmonic form $\omega$ of class $B^r$. This claim identifies harmonic chainlets precisely as the chainlet representatives of harmonic differential forms under the $Ch$ correspondence; the supplied text does not establish whether it is proved or remains open.