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The electroweak symmetry-breaking sector is one of the most promising and uncharted parts Standard Model (SM); but it seems likely that new physics may be out reach present accelerator effort hope to observe small deviations from SM. Given that, effective field theory (EFT) becomes logic method use, (SMEFT) has become standard. However, general with known particle content Higgs (HEFT), whether SMEFT suffices should investigated in future experimental efforts. Building on investigations by other groups established geometric criteria distinguish HEFT (useful for theorists examining specific beyond-SM completions), we seek more phenomenological understanding an analogous discussion aimed at a broader audience. We discuss various aspects (multi)Higgs boson production longitudinal gauge bosons ${W}_{L}{W}_{L}\ensuremath{\rightarrow}n\ifmmode\times\else\texttimes\fi{}h$ TeV region as necessary information characterize flare function, $\mathcal{F}(h)$, determines or needed. also tree-level amplitudes including contact exchange channels, well short accessing $\mathcal{F}$ statistical limit many bosons. status coefficients series expansion its validity, complex-$h$ extension can used predict not tell-tale zero, how they relate dimension-six -eight operators sector. derive set correlations among beyond standard model corrections help decide, data, have viable SMEFT. This analysis useful machines LHC could address challenging final state several