The central-charge norm identity

This does not authorize shifting or renormalizing the canonical $L_0$ in a VOA identity. It separates that fixed operator from an additional physical units and clock assignment.

A polynomial bound of order $k$ also implies every weaker bound of order $k^{\prime }\ge k$, because $1+L_0\ge 1$. Consequently the existence of one displayed polynomial exponent is not an intrinsic gravitational observable.