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Abstract

Measurements of single-, double-, and triple-differential cross-sections are presented for boosted top-quark pair-production in 13$~\text{TeV}$ proton--proton collisions recorded by the ATLAS detector at the LHC. The top quarks are observed through their hadronic decay and reconstructed as large-radius jets with the leading jet having transverse momentum ($p_{\text{T}}$) greater than 500$~$GeV. The observed data are unfolded to remove detector effects. The particle-level cross-section, multiplied by the $t\bar{t} \rightarrow W W b \bar{b}$ branching fraction and measured in a fiducial phase space defined by requiring the leading and second-leading jets to have $p_{\text{T}} > 500~$GeV and $p_{\text{T}} > 350~$GeV, respectively, is $331 \pm 3 \text{(stat.)} \pm 39 \text{(syst.)}~$fb. This is approximately 20\% lower than the prediction of $398^{+48}_{-49}~$fb by Powheg+Pythia$~$8 with next-to-leading-order (NLO) accuracy but consistent within the theoretical uncertainties. Results are also presented at the parton level, where the effects of top-quark decay, parton showering, and hadronization are removed such that they can be compared with fixed-order next-to-next-to-leading-order (NNLO) calculations. The parton-level cross-section, measured in a fiducial phase space similar to that at particle level, is $1.94 \pm 0.02 \text{(stat.)} \pm 0.25 \text{(syst.)}~$pb. This agrees with the NNLO prediction of $1.96^{+0.02}_{-0.17}~$pb. Reasonable agreement with the differential cross-sections is found for most NLO models, while the NNLO calculations are generally in better agreement with the data. The differential cross-sections are interpreted using a Standard Model effective field-theory formalism and limits are set on Wilson coefficients of several four-fermion operators.