jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pMeasurements of single-, double-, and triple-differential cross-sections are presented for boosted top-quark pair-production in 13 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 (jats:italicp</jats:italic>jats:subT</jats:sub>) greater than 500 GeV. The observed data are unfolded to remove detector effects. The particle-level cross-section, multiplied by the jats:inline-formulajats:alternativesjats:tex-math$$ t\overline{t}\to WWb\overline{b} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mit</mml:mi> mml:mover mml:mit</mml:mi> mml:mo¯</mml:mo> </mml:mover> mml:mo→</mml:mo> mml:miWWb</mml:mi> mml:mover mml:mib</mml:mi> mml:mo¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula> branching fraction and measured in a fiducial phase space defined by requiring the leading and second-leading jets to have jats:italicp</jats:italic>jats:subT</jats:sub>jats:italic></jats:italic> 500 GeV and jats:italicp</jats:italic>jats:subT</jats:sub>jats:italic></jats:italic> 350 GeV, respectively, is 331 jats:italic±</jats:italic> 3(stat.) jats:italic±</jats:italic> 39(syst.) fb. This is approximately 20% lower than the prediction of jats:inline-formulajats:alternativesjats:tex-math$$ {398}{-49}^{+48} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msubsup mml:mn398</mml:mn> mml:mrow mml:mo−</mml:mo> mml:mn49</mml:mn> </mml:mrow> mml:mrow mml:mo+</mml:mo> mml:mn48</mml:mn> </mml:mrow> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> fb by Pjats:scowheg</jats:sc>+Pjats:scythia</jats:sc> 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 1jats:italic.</jats:italic>94 jats:italic±</jats:italic> 0jats:italic.</jats:italic>02(stat.) jats:italic±</jats:italic> 0jats:italic.</jats:italic>25(syst.) pb. This agrees with the NNLO prediction of jats:inline-formulajats:alternativesjats:tex-math$$ {1.96}{-0.17}^{+0.02} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msubsup mml:mn1.96</mml:mn> mml:mrow mml:mo−</mml:mo> mml:mn0.17</mml:mn> </mml:mrow> mml:mrow mml:mo+</mml:mo> mml:mn0.02</mml:mn> </mml:mrow> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> 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.</jats:p>