= Solution
The <accreting-pulsar luminosity and material-torque consistency> test shows a concrete tension between the simplest isotropic <luminosity> estimate and the material-torque estimate. Making their rates equal requires
$$
\frac{r_{\rm Alf}}{r_{\rm co}}=\left(\frac{2.23}{48.6}\right)^2=2.11\times10^{-3},\qquad
\boxed{r_{\rm Alf}\simeq4.4\ \mathrm{km}<R_{\rm NS}}.
$$
An exterior <accretion Alfvén radius> cannot lie inside a 10-km star. Even taking its smallest exterior value, $r_{\rm Alf}=R$, the observed <torque> permits only about $32\dot M_{\rm Edd}$ in this model, below the $49\dot M_{\rm Edd}$ isotropic estimate. The discrepancy is modest enough to be sensitive to the approximate radius and moment of inertia, but it prevents claiming exact simultaneous agreement under the stated central values.
Near corotation, the <torque> gives only $2.23\dot M_{\rm Edd}$. If its <radiative efficiency> is unchanged, beaming into a fraction about $2.23/48.6\simeq0.046$ of the sky would reconcile that intrinsic <luminosity> with the apparent isotropic value. The given truncation formula would then require $B\sim2.6\times10^8$ T for a magnetosphere near corotation. Other possibilities include substantial opposing magnetic <torque>, outflows separating the disk supply rate from the surface rate, a different <radiative efficiency> and magnetically altered <opacity>. These are changes to the elementary model that need independent evidence, rather than a license to use an unphysical truncation radius. Coherent pulsations already identify the accretor as a <neutron star>; they do not by themselves choose between these accretion-flow refinements.
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