A recent analysis of data on the two photon production of the $eta_c$ and its decay to $K(Kpi)$ has determined the $Kpi$ $S$-wave amplitude in a model-independent way assuming primarily that the additional kaon is a spectator in this decay. The purpose of this paper is to fit these results, together with classic $Kpi$ production data from LASS, within a formalism that implements unitarity for the di-meson interaction. This fixes the $I=1/2$ $Kpito Kpi$ $S$-wave amplitude up to 2.4 GeV. This resolves the Barrelet ambiguity in the original LASS analysis, and constrains the amount of inelasticity in $Kpi$ scattering, highlighting that this becomes significant beyond 1.8 GeV. This result needs to be checked by experimental information on the many inelastic channels, in particular $Keta^prime$ and $Kpipipi$. Our analysis provides a single representation for the $Kpi$ $S$-wave from threshold, controlled by Chiral Perturbation Theory, through the broad $kappa$, $K_0^*(1430)$ and $K_0^*(1950)$ resonances. There is no arbitrary sum of Breit-Wigner forms and random backgrounds for real $Kpi$ masses. Rather the form provides a representation that can be translated to other processes with $Kpi$ interactions with their own coupling functions, while automatically maintaining consistency with the chiral dynamics near threshold, with the LASS data and the new results on $eta_c$ decay.
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