Bootstrapping <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> conformal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>QED</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We present the results of a conformal bootstrap study presumed unitary IR fixed point quantum electrodynamics in three dimensions (QED$_3$) coupled to $N_f=4$ two-component Dirac fermions. Specifically, we four-point correlators $SU(4)$ adjoint fermion bilinear $r$ and monopole lowest topological charge $\mathcal{M}_{1/2}$. Most notably, scaling $\mathcal{M}_{1/2}$ are found be constrained into closed island with combination spectrum assumptions inspired by $1/N_f$ perturbative as well novel interval positivity constraint on next-lowest-charge $\mathcal{M}_1$. Bounds this $U(1)_t$ conserved current central charges $c_J$, $c_J^t$, stress tensor $c_T$, comfortably consistent results. Together dimensions, suggests that part estimates from expansion -- even at provide self-consistent solution crossing relations, despite some our not being strictly justified.